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Finding truths is good, but without being handed down to posterity, truths will be lost into oblivion.
Topics
About:
truth
About:
humanity
The table of contents of this article
Starting Context
Target Context
-
The reader will understand that he or she can be a benefactor of humanity by being a conduit of truths.
Orientation
There is an article on that what we are supposed to do is to maintain the unboundedly consistent hypotheses system.
There is an article on that to establish the unbounded consistency is the only way to near truths.
There is an article on the distinctions between the reality, observations, and interpretations of observations, and where relativity, ambiguity, or unpredictability could exist.
Main Body
Stage Direction
Here is Special-Student-7 in a room in an old rather isolated house surrounded by some mountains in Japan.
1: Finding Truths Is Good, but Truths Without Being Handed Down Will Be Lost into Oblivion
Special-Student-7-Hypothesizer
Finding truths is good, but no truth shines by itself.
Special-Student-7-Rebutter
That depends on what is meant by "shine".
Special-Student-7-Hypothesizer
I mean that the truth is seen by some people.
Special-Student-7-Rebutter
Ah, I understand.
Special-Student-7-Hypothesizer
I think that any truth is valuable by itself even without being seen, but being valuable is not shining, in my expression.
Special-Student-7-Rebutter
Should a truth shine?
Special-Student-7-Hypothesizer
Yes, at least feebly, I say.
Look, I do not expect a more important truth to shine brighter; for example, I do not expect a science book full of truths to be read more than a vacuous manga book to be, and it is OK, but if the book is not read at all, the book will not be handed down to posterity, which is not OK.
Special-Student-7-Rebutter
So, 'not shine at all' and 'shine extremely feebly' are critically different: however feebly it is, the truth could be handed down to posterity as far as the truth is shining.
Special-Student-7-Hypothesizer
In fact, I think that the fact that no truth shines by itself is a firm proof that no fair God exists: if a fair God existed, It certainly would make any truth shine, at least feebly.
Special-Student-7-Rebutter
Are you sure that It is not making a truth shine feebly?
Special-Student-7-Hypothesizer
Well, I said "at least feebly", but I do not see why It can help but make a truth shine as bright as it deserves, and I know that many truths are not being made shine as bright as it deserves, so I am pretty sure that no fair God exists.
2: The Disproportionality of Popularity Systems, Especially Search Engines
Special-Student-7-Hypothesizer
But the problem is that it is quite difficult for a truth to shine feebly on the Bias Planet, as that kind of popularity systems prevail there.
Special-Student-7-Rebutter
What do you mean by "that kind of popularity systems"?
Special-Student-7-Hypothesizer
For example, typical (or probably all the) search engines, which JUST (at least mostly) present more popular items in higher precedence.
Special-Student-7-Rebutter
You should elaborate what the matter is with it.
Special-Student-7-Hypothesizer
Let us suppose that there are some items of deserved-popularities of 13%, 12%, 11%, 10%, 9%, 8%, 7%, 6%, 5%, 4%, 3%, 2%, 1%, 0.5%, . . ., listed in that order in a search result.
Special-Student-7-Rebutter
What is "deserved-popularity"?
Special-Student-7-Hypothesizer
If all the items were given even opportunities, a 1% deserved-popularity item would take the 1% popularity.
Special-Student-7-Rebutter
Ah, the point is that the realized-popularity is so, not purely because of the deserved-popularity, but very significantly because of the amount of the given opportunities.
Special-Student-7-Hypothesizer
The top 13% deserved-popularity item most probably will not take just the 13% popularity, but a disproportionally much higher popularity, for example 60% popularity.
On the other hand, the 1% deserved-popularity item will not take the 1% popularity, but an almost 0 popularity, especially because it is not on the 1st result page.
In that kind of system, it is quite difficult for a 1% deserved-popularity item to shine even feebly.
Look, we are really OK that we do not take the most popularity; we really do not aim much popularity at all; we are just hoping to reach the 1% selected persons, but it is quite difficult in that kind of system.
Special-Student-7-Rebutter
In fact, search engines do not (whether cannot or will not) assess the deserved popularities based on the contents, but are judging what are popular based on being already popular, which are popular just because the search engines have determined to be popular.
Special-Student-7-Hypothesizer
"More important items should have more back links." is really bull shit: it is only after all the items are given even opportunities that such a correlation ensues, while the search engine itself prevents such opportunities.
So, "organic back-links-building" is really absurd, because a no-back-link-right-now item is not seen by anyone, and the item not seen by anyone cannot get back links "organically".
Special-Student-7-Rebutter
I guess that most (or at least many) people have notices the situation, but enigmatically to me, such "bull shit" keeps prevailing on the Bias Planet . . .
3: There Is a Potential Improvement for Search Engines, but . . .
Special-Student-7-Hypothesizer
Obviously, just listing items in the deserved-popularities order does not realize the proportionate attentions.
Special-Student-7-Rebutter
Even if the deserved-popularities are supposed to have been justly assessed.
Special-Student-7-Hypothesizer
Yes, let them be supposed so, for now.
The only solution seems to be to list the 1% deserved-popularity item at the top for the 1% persons.
Special-Student-7-Rebutter
That is to customize search results for each person, which seems to be already being somehow attempted by some search engines.
Special-Student-7-Hypothesizer
The problem is that those search engines thrust what they decide each person should want, not offer what each person really wants.
Special-Student-7-Rebutter
In fact, they should let each person explicitly specify what he or she wants, not surreptitiously gather data and do second-guessing.
Special-Student-7-Hypothesizer
They refuse to do so, because they are trying to trick each person into buying what they want to sell (more specifically, what advertisers who paid to them want to sell), not trying to offer what each person really wants.
Special-Student-7-Rebutter
What we are saying is that there should be some detailed search options each person can explicitly choose.
Special-Student-7-Hypothesizer
Options like "I want truths instead of fake news.", "I want rigidly logical explanations instead of intuitive not-exact explanations.", "I don't want advertisements.", etc. .
Special-Student-7-Rebutter
The last option is what major search engines will refuse to offer.
Special-Student-7-Hypothesizer
I guess so.
Special-Student-7-Rebutter
And would many people choose the "I want fake news." option?
Special-Student-7-Hypothesizer
Why not? They would not be able to see what they wanted unless they had chosen the option.
Special-Student-7-Rebutter
An issue is whether search engines can discern fake news, intuitive not-exact explanations, etc., technically speaking.
Special-Student-7-Hypothesizer
If they cannot, a way is to let authors put in meta tags.
Special-Student-7-Rebutter
Would many authors put in the "this is fake-oriented" meta tag?
Special-Student-7-Hypothesizer
Why not? Unless they do so, they would not be able to reach the potential readers.
Special-Student-7-Rebutter
Well, I see a point, but the people who love fake news love fake news because they do not admit that the fake news are fake.
Special-Student-7-Hypothesizer
The option does not need to be expressed exactly "I want fake news.", but be an euphemism.
Special-Student-7-Rebutter
"an euphemism" . . . like . . .
Special-Student-7-Hypothesizer
I do not know; I am not so an euphemist. Well, perhaps "I believe that it is sometimes necessary to fib a little"?
Special-Student-7-Rebutter
"sometimes" or "as frequently as one can possibly get away with it"?
Special-Student-7-Hypothesizer
You know, it is an euphemism.
Special-Student-7-Rebutter
"a little"?
Special-Student-7-Hypothesizer
'a lot', in other words.
Anyway, I am really OK that fake news are presented to fake news lovers, but please not present fake news to me or some other non-'fake news lovers', just because fake news are popular.
Special-Student-7-Rebutter
Is there any tiny hope that a search engine will implement such options?
Special-Student-7-Hypothesizer
Not from major search engines that target majority, but I wonder why a conscientious minor search engine cannot appear.
Special-Student-7-Rebutter
It will have to be minor . . .
Special-Student-7-Hypothesizer
I think that it will be inevitably minor.
Special-Student-7-Rebutter
It is important that such a minor search engine is known to some selected persons who should know it.
Special-Student-7-Hypothesizer
Certainly, that is an issue: as the 1% deserved-popularity item is not seen by the 1% people, the 1% deserved-popularity search engine is not known to the 1% people. In fact, a promising minor search engine may exist, although we do not know it.
4: What Are Meant by "Truth"?, by the Way
Special-Student-7-Hypothesizer
Many Biasians seem not to even believe that there is a distinction between truths and non-truths, nowadays.
Special-Student-7-Rebutter
Ah, "post-truth" . . .. I wonder whether they are so ignorant to not understand the distinction or they are so rotten to not admit the distinction as they understand the distinction.
Special-Student-7-Hypothesizer
Well, they are certainly ignorant to not understand the distinction, but they persist to keep being ignorant because they are so rotten to want to not admit the distinction. They want to not admit the distinction, because they want to claim whatever they want to claim, because if there was no non-truth, whatever blatant lies they claimed would not be lies.
Special-Student-7-Rebutter
So, they adamantly refuse to be enlightened . . .
Special-Student-7-Hypothesizer
I wonder whether they cannot be forced to be enlightened by clearly showing how they are wrong. I mean, can someone persist to claim that the Bias Planet is a flat plane after being clearly shown that that is not the case?
Special-Student-7-Rebutter
The knowledge had taken much time to be spread while being a flat plane is not particularly so convenient for many people. On the other hand, nonexistence of the distinction is so convenient for many people to be easily given up.
Special-Student-7-Hypothesizer
Anyway, how they are wrong is that they do not distinguish the reality, observations, and interpretations of observations.
Special-Student-7-Rebutter
Certainly.
Special-Student-7-Hypothesizer
A typical case of fallacy is that a president of a country claims that more people came to his or her inaugural address than to his or her predecessor's, while that is not really the case.
Special-Student-7-Rebutter
And he or she insists that his or her claim is an "alternative fact", because more people were really seen to have come, from his or her perspective?
Special-Student-7-Hypothesizer
It is really childish, but nevertheless very prevalent fallacy: it is just that "More people were seen to have come, from his or her perspective." may be a fact, but "More people came." is not any fact.
They claim like "As an object is seen in different ways in different perspectives, there are alternative facts.", but no!, 'The object is seen as a triangle in a perspective.' and 'The object is seen as a circle in another perspective.' are no alternative facts but 2 distinctly different facts.
Special-Student-7-Rebutter
They sloppily state like "The object is a triangle." or "The object is a circle." and claim that they are alternative facts, but no, they are not facts at all, although 'The object is seen as a triangle in a perspective.' and 'The object is seen as a circle in another perspective.' are facts.
Special-Student-7-Hypothesizer
Some people may claim that a truth has ceased to be a truth as some conditions have changed.
Special-Student-7-Rebutter
They think so because they think sloppily. The real truth in that case is really conditional like "If A then B." while they think that the truth is "B"; as "A" has ceased to hold, "B" has ceased to be true, but "If A then B." has not ceased to be true at all; "B" has never been really a truth. . . . If someone does not understand that, he or she should learn logic.
Special-Student-7-Hypothesizer
A similar fallacy is "A truth does not exist just because humans do not (or cannot) know it.".
Special-Student-7-Rebutter
That fallacy is ludicrous, but seems to have been traditionally very popular on the Bias Planet.
Special-Student-7-Hypothesizer
For them, an electron in a black hole does not exist just because humans cannot know the existence. . . . How selfish someone can be!
A claim like "As humans cannot know the position of an electron, the electron is in a state that the position is not determined." is in the same category. Actually, the electron is not in that state, but humans are in the state that they do no know the position.
Such a claim inevitably leads to a conclusion like "As humans cannot know whether a cat is alive or dead, the cat is a zombie."
Special-Student-7-Rebutter
Some people may claim "Whether a truth exists or not, as humans cannot know it for sure, you cannot claim that something is a truth.".
Special-Student-7-Hypothesizer
So, are they allowed to claim blatant lies?
1st, even if some things are not known to be absolutely true, blatant lies are known to be absolutely untrue.
2nd, while we have not reached an absolute truth (and we may not be able to reach an absolute truth), we can endlessly approach the absolute truth, which is what we are supposed to do.
Special-Student-7-Rebutter
Some people are like "As nothing is proved to be absolutely true, all the claims are equal.". . . . No. Any inconsistent claim is absolutely untrue; a seems-to-be-consistent-for-now claim may eventually turn out to be untrue, but it is an approach to a truth.
Special-Student-7-Hypothesizer
The latter is a hypothesis, and the only type of sincere approaches is to maintain an unboundedly consistent hypothesis.
Special-Student-7-Rebutter
Being unbounded is the point.
Special-Student-7-Hypothesizer
So, certainly, what we call "truth" may turn out be a non-truth, but "truth" is at least an unboundedly consistent hypothesis.
If somebody says that that use of "truth" is sloppy, well, I agree actually, but there is no word for 'unboundedly consistent hypothesis' on the Bias Planet, and "truth" is actually almost always an unboundedly consistent hypothesis, so, we are compromising to grudgingly use "truth" that way.
5: You Can Be a Benefactor of Humanity by Being a Conduit of Truths
Special-Student-7-Hypothesizer
As there is no fair God that makes truths shine and search engines are not much helpful in making truths shine, it is only you that can make a truth shine.
Special-Student-7-Rebutter
How?
Special-Student-7-Hypothesizer
You can spread a truth by word of mouth.
Special-Student-7-Rebutter
Does it have to be offline?
Special-Student-7-Hypothesizer
No. I do not mean literally "by mouth", but mean that you do it individually. So, writing about the truth in your blog, a Q & A site, or something is a kind of "word of mouth".
Special-Student-7-Rebutter
It is important not to assume that the truth will be automatically spread by an authority, like God or a search engine.
Special-Student-7-Hypothesizer
The humanity is depending on you to spread the truth.
References
<The previous article in this series | The table of contents of this series | The next article in this series>
<The previous article in this series | The table of contents of this series | The next article in this series>
A red marble is no less red just because it is lumped in an all-the-others-are-blue population. It is not responsible for the others' being blue.
Topics
About:
bias
About:
probability
The table of contents of this article
Starting Context
Target Context
-
The reader will understand that judging an individual based on the others of any population is injustice.
Orientation
What we are supposed to do is to maintain the unboundedly consistent hypotheses system.
To establish the unbounded consistency is the only way to near truths.
Main Body
Stage Direction
Here is Special-Student-7 in a room in an old rather isolated house surrounded by some mountains in Japan.
1: A Red Marble Is No Less Red, Lumped in Whatever Population
Special-Student-7-Hypothesizer
Here is a red marble.
Special-Student-7-Rebutter
I do not see any marble, to say nothing of a red marble
Special-Student-7-Hypothesizer
Suppose that here is a red marble.
Special-Student-7-Rebutter
OK.
Special-Student-7-Hypothesizer
It is very red.
Special-Student-7-Rebutter
How very red?
Special-Student-7-Hypothesizer
It is redder than you can imagine.
Special-Student-7-Rebutter
. . .
Special-Student-7-Hypothesizer
It is very red.
Special-Student-7-Rebutter
I understand that.
Special-Student-7-Hypothesizer
It is no less red just because it is lumped together with 99 very blue marbles.
Special-Student-7-Rebutter
Of course.
Special-Student-7-Hypothesizer
The population is said to be 99% blue.
Special-Student-7-Rebutter
That statement is correct.
Special-Student-7-Hypothesizer
But the very red marble is not 99% blue.
Special-Student-7-Rebutter
Of course: it is very red.
Special-Student-7-Hypothesizer
It is redder than you are.
Special-Student-7-Rebutter
I am not particularly red.
Special-Student-7-Hypothesizer
Then, all the more it is redder than you are.
Anyway, it is an absurd injustice for you to blame the very red marble just because it is lumped in the 99% blue population, because the very red marble is far more redder than you are.
Special-Student-7-Rebutter
Of course, even if we suppose that being blue is something to be blamed.
2: A Very Sweet Apple of a Not-So-Sweet-on-Average Kind Is Sweeter Than Most Apples of a Sweet-on-Average Kind
Special-Student-7-Rebutter
Some people would say "I have not arbitrarily lumped a red marble with 99 blue marbles; I am talking about a kind of apples."
Special-Student-7-Hypothesizer
Would they mean that the choice of the population was logical?
Special-Student-7-Rebutter
They should mean so; as all the apples of a kind shared the same set of genes, they would share the traits.
Special-Student-7-Hypothesizer
But we have some evidences that a tree bears sweeter fruits than another tree of the same kind does, because of soil, sunshine, temperatures, water, care, etc..
Special-Student-7-Rebutter
On average, you mean.
Special-Student-7-Hypothesizer
On average, I mean; also from a tree, a fruit is sweeter than another, because there are good branches and bad branches, there are good buds and bad buds, sunshine is not uniform, some leaves are eaten by worms, etc..
Usually, amounts like sweetness are distributed according to bell curves, and a very sweet apple of a not-so-sweet-on-average kind is sweeter than most apples of a sweet-on-average kind.
3: The Individuals of a Human Race Are Not a Bunch of Clones
Special-Student-7-Hypothesizer
Besides, while all the apple trees of a kind are a bunch of clones, the individuals of a human race are not so.
Special-Student-7-Rebutter
To inform someone who does not know, the tree grown from a seed of the kind is not of the kind.
Special-Student-7-Hypothesizer
As any human child does not have the exactly same set of genes of a parent, the tree grown from a seed does not have the exactly same set of genes of the parent.
So, any tree of the kind is made only by grafting a twig of the kind onto a stock, which has been grown from a seed.
Special-Student-7-Rebutter
Then, the upper part of the tree certainly has the genes of the kind, a crone.
Special-Student-7-Hypothesizer
What everybody has to know is that while a clone apple of a not-so-sweet-on-average kind cannot be truthfully prejudged to be not sweet, a non-clone individual of a human race can be less truthfully prejudged to be incompetent, unworthy, or a lawyer.
4: We Sincerely Suspect That There Are Some Differences in AVERAGE Born-Intelligence Across Races, but . . .
Special-Student-7-Hypothesizer
This may be controversial somewhat, but I sincerely say this because I am disgusted with lies even if beautiful: I suspect that there are some differences in average born-intelligence across races (note that I had "average" in place).
That is because it is quite unnatural to suspect otherwise: while skin color, height, etc. are influenced by some genes, is only born-intelligence not influenced by any gene at all? . . . Let us refrain from such a blatant lie.
Special-Student-7-Rebutter
I guess that average born-intelligences cannot be exactly the same across races, although I have no data to estimate the extent of the differences.
Special-Student-7-Hypothesizer
I think that there is a reasonable possibility that a too benevolent environment has indulged genes of a race a little, because relatively less intelligence could be required to survive in such an environment.
Special-Student-7-Rebutter
Well, that sounds plausible on 1st impression, although I do not lightly adopt that as my hypothesis.
Special-Student-7-Hypothesizer
Anyway, I have dared to disclose the suspicion not in order to disparage a race; on the contrary, my intention is to refute disparagement based on the suspicion.
I do not think that blatant "beautiful" lies like "All are equal." will eliminate biases; if such lies prevail outwardly, biases will dig in inwardly and prevail there.
Special-Student-7-Rebutter
I agree that unless a bias is revealed where it is really wrong, the bias will survive, if hidden.
Special-Student-7-Hypothesizer
A cure of the bias is, as expected, that a person of a not-so-intelligent-on-average race is more intelligent than most of an intelligent-on-average race.
Special-Student-7-Rebutter
That is a statistical fact.
Special-Student-7-Hypothesizer
The other cure is that born-intelligence is less decisive than learning is.
In fact, a learned person with not-so-high-born-intelligence is usually less stupid than an unlearned one with high-born-intelligence.
Special-Student-7-Rebutter
In my estimation, born-intelligence is mostly about efficiency for learning; certainly, high efficiency is very desirable, but high efficiency is nothing for anybody who does not learn in the 1st place, and while it may be hard for a person with low-born-intelligence to exceed a person with high-born-intelligence who learns hardest, considering the situation that most people do not learn hard enough, it is really possible for a person with low-born-intelligence to exceed most people.
5: It Is an Exception? So What?
Special-Student-7-Rebutter
Some people seem to dismiss a very sweet apple of a not-so-sweet-on-average as just an exception.
Special-Student-7-Hypothesizer
It is an exception, so what?
Special-Student-7-Rebutter
They say "There are always some exceptions.".
Special-Student-7-Hypothesizer
So what?
Being an exception does not make the apple any less sweet; how in the hell could someone possibly imagine that treating a very sweet apple as though it was not sweet could escape being an injustice?
Special-Student-7-Rebutter
Someone will bring up "joint liability", perhaps?
Special-Student-7-Hypothesizer
Absurd! Please take some rest from being irrational! The very sweet apple is not in any way responsible for another apple's being not sweet.
Special-Student-7-Rebutter
Certainly, "joint liability" is irrational, but it is really prevalent on the Bias Planet, partly because it is a typical method for corner-cutting.
Special-Student-7-Hypothesizer
Ah, I know; someone does not want to bother to attend to each individual, so, he or she roughly lumps individuals together in a population and treat all the members of the population indiscriminately. He or she is saying "You should suffer injustices in order for me to do corner-cuttings.".
Special-Student-7-Rebutter
Yes, and rulers especially tend to love "joint liability", because they can delegate the work of watching individuals to each group whose members desperately watch each other in order for themselves to be not punished because of other members.
Special-Student-7-Hypothesizer
Why the hell must I be punished just because I have happened to be lumped together with a naughty guy?
Special-Student-7-Rebutter
It is really unjust, but rulers do not care being unjust.
Special-Student-7-Hypothesizer
Even "God" seems to be a fan of corner cuttings: why must the descendants of Adam be punished just because Adam ate an apple? Let Adam solely take the blame. It is a "joint liability"; it is absurd; it is unjust.
6: Intellectual Laziness Is a Sin
Special-Student-7-Hypothesizer
We can call the propensity for corner-cuttings 'laziness' in another word.
I find that intellectual laziness is really a problem.
That is because as someone does corner-cuttings in recognitions, he or she harbors a wrong world view, and anyone who acts on any wrong world view cannot help but do injustices to others.
Special-Student-7-Rebutter
Certainly.
Special-Student-7-Hypothesizer
Some people may be thinking that although laziness is certainly not laudable, in fact deplorable, it is not particularly a sin, but they are greatly mistaken.
Special-Student-7-Rebutter
Yes.
Special-Student-7-Hypothesizer
While there are many people who hate to study, they inevitably do injustices based on wrong world views. Anyone simply cannot form any decent world view without studying, and simply cannot act justly based on wrong world views.
Special-Student-7-Rebutter
Certainly.
Special-Student-7-Hypothesizer
Having benevolence is not enough; sound understandings are required.
Special-Student-7-Rebutter
Yes.
Special-Student-7-Hypothesizer
. . . Can you say only "Certainly" and "Yes"?
Special-Student-7-Rebutter
Well, it is just that there is nothing to rebut.
To elaborate more, there is no such thing as a "benevolence" that is OK with not studying while studying is indispensable for acting justly.
7: Any Population Is a Somewhat Arbitrary Intrusion
Special-Student-7-Hypothesizer
Any individual is an individual.
Special-Student-7-Rebutter
Of course.
Special-Student-7-Hypothesizer
An individual is not particularly a Thai.
Special-Student-7-Rebutter
I think, someone is.
Special-Student-7-Hypothesizer
I mean, an individual is certainly a Thai, but also is a male, a foot fetishist, a lawyer, or something.
Special-Student-7-Rebutter
I guess, someone is.
Special-Student-7-Hypothesizer
He is not particularly a foot fetishist.
Special-Student-7-Rebutter
I think, he is.
Special-Student-7-Hypothesizer
I mean, he certainly is, but does not need to be judged by a statistical distribution of the population of foot fetishists.
Special-Student-7-Rebutter
Well, judging with the population of lawyers may not be kinder.
Special-Student-7-Hypothesizer
Anyway, whatever population with which you judge him is somewhat arbitrary and an intrusion.
Special-Student-7-Rebutter
A usual stratagem is for you to pick up a population that gives an impression convenient for your purpose, but another population may just give a rather opposite impression.
8: What Is Permitted Is Just to Be Careful, Without Abuse
Special-Student-7-Rebutter
Some people will say "But, shouldn't I be careful when a population is 99% terrorists?".
Special-Student-7-Hypothesizer
I think that they should, . . . so what?
A usual tactic by evil people is to twist a concept: being careful is just being careful, not treating a might-not-be-a-terrorist person as a terrorist.
Just be careful without any abuse.
References
<The previous article in this series | The table of contents of this series | The next article in this series>
<The previous article in this series | The table of contents of this series | The next article in this series>
Having won a bet is a matter of luck, not your feat, although fairly estimating an effective probabilities distribution can be a feat.
Topics
About:
bias
About:
probability
The table of contents of this article
Starting Context
Target Context
-
The reader will understand that claiming credit for having won a bet is ludicrous and very harmful.
Orientation
What we are supposed to do is to maintain the unboundedly consistent hypotheses system.
To establish the unbounded consistency is the only way to near truths.
Main Body
Stage Direction
Here is Special-Student-7 in a room in an old rather isolated house surrounded by some mountains in Japan.
1: Having Won a Bet Is Not Your Feat
Special-Student-7-Hypothesizer
A very ludicrous act is to claim credit for having won a bet.
Special-Student-7-Rebutter
Do you mean that someone says that having won the bet is his or her feat?
Special-Student-7-Hypothesizer
He or she says so directly or indirectly.
Special-Student-7-Rebutter
When you say "indirectly" . . .
Special-Student-7-Hypothesizer
He or she boasts of his or her having won the bet.
Special-Student-7-Rebutter
Certainly, if he or she did not think that it was his or her feat, there would be no reason to boast of it.
Special-Student-7-Hypothesizer
We are talking not only about dice bets, roulette, etc. but also about trading stocks, predicting the winner of a baseball league season, assuming that someone is a thief, in fact, assuming anything not on absolutely solid grounds.
Special-Student-7-Rebutter
Although betting one's own money on dice is just a personal matter, assuming that someone is a thief is a serious matter.
Special-Student-7-Hypothesizer
Does someone not understand that winning any bet is a matter of luck?
Special-Student-7-Rebutter
The problem is that someone boasts of having won a single bet.
Special-Student-7-Hypothesizer
If the results of a significant number of tries fairly approximate your probabilities distribution estimation, you may be able to legitimately boast of having made the estimation, but boasting of a single win is ludicrous.
2: The Mentality Entails Grave Harm, in Fact
Special-Student-7-Rebutter
The mentality of claiming credit for having won a bet is of course laughable, but it is not something to be let pass as simply amusing.
Special-Student-7-Hypothesizer
The mentality means that the person is assuming that he or she possesses some supernatural power that can tell things not on absolutely solid grounds, which is really a grave problem.
In fact, he or she begins to declare that someone is a thief, a terrorist, or a lawyer, not on absolutely solid grounds.
Assuming to possess some supernatural power may seem an innocent ignorance, but falsely declaring someone to be a thief, or a lawyer, is hardly "innocent".
Special-Student-7-Rebutter
Being ignorant more or less is of course unavoidable for tiny-brained humans, but not admitting one's ignorance is really a sin.
3: Let Us Understand the Concept of Probability, Correctly
Special-Student-7-Rebutter
We all have to understand the concept of probability correctly, because while almost all the matters in human life have to be judged probabilistically, if some people do not understand the concept of probability correctly, what kinds of injustices are being performed daily?
Special-Student-7-Hypothesizer
Serious kinds, I guess.
The most important thing to be always aware of about probability is that any probability depends on the choice of population.
For example, in the case of weather forecasting, the rain probability for any day is about choosing a significantly large population of some past days that resemble the concerned day and counting the days in which some rain had fallen.
Special-Student-7-Rebutter
"resemble" depends on the criteria by which some days are deemed to resemble the concerned day.
Special-Student-7-Hypothesizer
The choice of the criteria is essentially arbitrary; for example, all the days can be deemed to resemble the concerned day, in virtue of having 24 hours, which is a kind of criteria.
Then, the rain probability for the day will be just the yearly rain probability; I mean, if it rains 73 days in 365 days, the probability will be 20%.
Special-Student-7-Rebutter
If a weather forecaster does so for every day, the rain probabilities for all the days will be the same 20%, insipid, but not wrong in any way.
Special-Student-7-Hypothesizer
Usually, different populations are used for different days, which is the reason why the weather forecast for a day is different from the one for another day.
Special-Student-7-Rebutter
The population for each day is chosen by some criteria that are usually about distributions of cloud, temperature, pressure, etc.
Special-Student-7-Hypothesizer
It is important to understand that probability is about human ignorance, at least usually.
For example, it is in fact determined whether it will rain tomorrow or not, although humans cannot know it in their technology, because the phenomenon is too complex for them to be able to grasp the full initial condition and compute the future based on the full initial condition.
Special-Student-7-Rebutter
There will be some people who claim that indeterministicness of quantum mechanics is not about human ignorance.
Special-Student-7-Hypothesizer
In fact, I do not buy that claim, but anyway, I put "at least usually" in view of the claim.
At least, uncertainties of weather forecasts, earthquake predictions, etc. are not the consequences of quantum phenomena, at least mainly.
Whether an earthquake happens when is determined, although humans do not have the ability to know it.
4: Of Course, There Are Effective Populations and Ineffective Populations, Though
Special-Student-7-Hypothesizer
I said "The choice of the criteria is essentially arbitrary", but of course, there are effective populations and ineffective populations.
Special-Student-7-Rebutter
What populations are effective?
Special-Student-7-Hypothesizer
Decisive populations, I say: if it is nearly 100% rain or nearly 0% rain for the population, the population is decisive.
Special-Student-7-Rebutter
The population has to have a significant size as a precondition.
Special-Student-7-Hypothesizer
Of course.
But I wonder whether I am allowed to choose any skewed population if the population is decisive.
Special-Student-7-Rebutter
That depends on your purpose, I think.
Special-Student-7-Hypothesizer
What do you mean?
Special-Student-7-Rebutter
If your purpose is solely to predict the outcome, however skewed population will be fine, if it is really decisive.
Special-Student-7-Hypothesizer
What else could my purpose be?
Special-Student-7-Rebutter
Your purpose could be to claim a statistical distribution.
For example, you may claim that the crime rate for a race is high.
Special-Student-7-Hypothesizer
But the crime rate for every race may be high . . .
Special-Student-7-Rebutter
It will be naturally guessed that the population has been chosen so with a necessity, so, it will be naturally guessed that the crime rate is high only for the race.
Your claim is not particularly wrong, but it is maliciously misleading.
Special-Student-7-Hypothesizer
So, we should not unnecessarily narrow the population.
5: Sampling Has to Be Done Fairly
Special-Student-7-Rebutter
Let us not confuse sample with population: taking a smaller sample of the population is OK, because it is often difficult to survey the whole population, and taking a smaller sample is not narrowing the population.
Special-Student-7-Hypothesizer
But the sampling should not be skewed anyway, of course.
Special-Student-7-Rebutter
Skewing of sampling is more malicious, because it can be done utterly surreptitiously: some undesired samples can be just ditched secretly.
Special-Student-7-Hypothesizer
Someone can ditch some undesired samples in order to draw his or her pre-desired conclusion.
And it can be easily done as he or she can just forget having picked up the sample; as in prevalent answers by politicians, he or she just does not have the memory!
Special-Student-7-Rebutter
We have to learn that human impressions should not be trusted, because people filter things egoistically or neurotically.
6: Beware of Statistical Frauds, but . . .
Special-Student-7-Hypothesizer
You should not be deceived by numbers as though any number should be accurate by sole virtue of being a number.
A statistical number may be of an unnecessarily narrowed population or by a skewed sampling.
Special-Student-7-Rebutter
Or the sampling may not have been large enough; you should not be taken in by any conclusion drawn based on any insignificant sampling.
Special-Student-7-Hypothesizer
On the other hand, there is an issue of whether one should spurn any statistical numbers he or she does not like, claiming that they are frauds.
Special-Student-7-Rebutter
1st, they can be frauds, but he or she cannot declare that they are frauds, not on absolutely solid grounds; 2nd, to not accept any number unless one personally confirms its accuracy is a legitimate attitude, I think, but rejecting undesired numbers while accepting desired numbers without confirming their accuracies is not legitimate at all.
References
<The previous article in this series | The table of contents of this series | The next article in this series>
<The previous article in this series | The table of contents of this series | The next article in this series>
While there are some people (a part, if not all, of so-called finitists) who claim that no irrational number exists, it is not about the reality.
Topics
About:
truth
The table of contents of this article
Starting Context
Target Context
-
The reader will understand what the fact that some amounts cannot be expressed as rational numbers means.
Orientation
There is an article on the reality, observations, and interpretations of them.
There is an article on the necessity for stating the major premise explicitly and honestly.
Main Body
Stage Direction
Here is Special-Student-7 in a room in an old rather isolated house surrounded by some mountains in Japan.
1: Does No Irrational Number Exist?
Special-Student-7-Hypothesizer
While we talked about a YouTube channel, "Insights into Mathematics", in an article (we said that the channel was very thought-provoking, being sometimes really educative, sometimes impressively beautiful, and sometimes absolutely unacceptable), the channel claims that no irrational number exists.
Special-Student-7-Rebutter
While the channel is sometimes very lucid, as it begins to argue against irrational numbers or some other certain things, it suddenly becomes so muddy that I cannot discern the logical structures of the arguments.
Special-Student-7-Hypothesizer
That is because the channel does not disclose the major premises.
The channel is like "As humans don't know well about big numbers, the natural numbers set doesn't exist!". Huh? There must be a major premise missing, like "Whatever humans don't know don't exist!".
The channel's objections against 'Cauchy sequence' and 'Dedekind cut' are mainly based on its objection against infinite sets, which is based on such hidden major premises, which are not shared by us, so, the arguments do not logically add up for us.
Special-Student-7-Rebutter
I cannot discern any reason why irrational numbers as finite algorithms do not exist.
Special-Student-7-Hypothesizer
The claim that not all the irrational numbers can be expressed as finite algorithms cannot of course dispute the irrational numbers that can be expressed as finite algorithms, and the fact that an irrational number can be expressed in multiple algorithms cannot of course deny the irrational number, as the fact that \(\frac{1}{3}\) can be expressed in multiple forms like \(\frac{2}{6}, \frac{3}{9}, . . .\) cannot deny \(\frac{1}{3}\).
Special-Student-7-Rebutter
That claim itself is dubious, as it may be just that the algorithm for an irrational number is not known to humans yet.
Special-Student-7-Hypothesizer
The only reason cited in the channel seems to be that irrational numbers as finite algorithms are cumbersome for calculations, if that could be called a reason.
Special-Student-7-Rebutter
There seems to be a hidden major premise like "Whatever cumbersome for humans don't exist!".
Special-Student-7-Hypothesizer
The channel is claiming also that the ticker tape of the infinite decimal of any irrational number cannot be contained in the universe, but also the ticker tape of the infinite decimal of \(\frac{1}{3}\) cannot be contained in the universe.
In fact, I do not see any essential difference between \(\frac{1}{3}\) and \(\sqrt{2}\), because any digit of each of them is determined, with only the difference of hardships for knowing it.
Special-Student-7-Rebutter
Obviously, the ticker tape tale can apply only to irrational numbers as infinite decimals by infinite choices, for which the ticker tape is the sole source of the determination of each number.
Special-Student-7-Hypothesizer
The real issue should be whether the infinite decimal is uniquely determined, not whether a finite algorithm exists, right?
Special-Student-7-Rebutter
I think so; a finite algorithm is just a way but not necessarily the only way of determining the infinite decimal.
Special-Student-7-Hypothesizer
I kind of agree that irrational numbers as infinite decimals by infinite choices are not valid, because such an infinite decimal is not determined until someone has finished choosing all the digits, which has not been done yet. The professor is talking about the ticker tape not able to be contained in the universe, but that is irrelevant; what is relevant is that nobody has finished choosing all the digits.
But an infinite decimal does not need to be determined by a human choosing all the digits digit by digit; obviously, fixing a finite algorithm determines the infinite decimal, but also fixing any more generally appropriate specification determines the infinite decimal.
Special-Student-7-Rebutter
When you say "more generally appropriate specification" . . .
Special-Student-7-Hypothesizer
For example, 'the diagonal length of unit square' is fine.
Special-Student-7-Rebutter
You mean, even if any algorithm is not presented, nevertheless, the amount is determined, which is what matters.
Special-Student-7-Hypothesizer
Yes. And also 'the height of this penguin' is fine.
Special-Student-7-Rebutter
Ah, it is not the matter of whether humans do or can know the exact height, you mean?
Special-Student-7-Hypothesizer
Yes. Whether humans do or can know the exact height does not influence the existence of the exact height in the reality, which is what matters. In fact, the penguin does not become taller or shorter just because I have mis-measured the height, or the penguin is not in a mysterious state of having no height just because I have neglected to measure the height.
Special-Student-7-Rebutter
That is the point we really disagree with the professor: he is like "Something doesn't exist just because humans don't know it!".
Special-Student-7-Hypothesizer
And each point on a coordinates axis determines the infinite decimal by virtue of existing there.
Special-Student-7-Rebutter
You mean, we, humans, do not need to pick up a point in order for the point to exist.
Special-Student-7-Hypothesizer
Of course: The point does not begin to exist as we have picked up the point, but as the point has existed, we can pick it up.
Special-Student-7-Rebutter
So, any irrational number is defined all right by a point on the axis.
Special-Student-7-Hypothesizer
It will be needless to say that it is not the matter of whether humans can know the exact coordinate of the point.
And if you begin to claim like "Humans can't draw any exact coordinate axis." or "Humans can't pick up any exact coordinate point.", I remind you that it is not about irrational numbers any more: you cannot do so for rational coordinates either.
2: Why Irrational Numbers Are Required
Special-Student-7-Hypothesizer
To answer to "Why irrational numbers are required?", for example, otherwise, the diagonal length of unit square would not exist.
Special-Student-7-Rebutter
The professor seems to be promoting using "quadrance" instead ('Math Foundations 133: Higher dimensions and the roles of length, area, and volume'), meaning that we should talk in terms of squares of length, instead of in terms of lengths.
Special-Student-7-Hypothesizer
But, using "quadrance" does not solve the problem. For example, extend the 2 "quadrance" diagonal with the 1 "quadrance" line segment, and the result line segment will be a \((\sqrt{2} + 1)^2\) "quadrance" line segment, with the irrational "quadrance". So, "quadrance" can be irrational anyway.
Special-Student-7-Rebutter
By the professor's mathematics, you cannot draw the 1 "quadrance" line segment in the diagonal direction, because he does not admit irrational numbers plane but rational numbers plane, in which the 1 "quadrance" line segment cannot exist in the diagonal direction.
Special-Student-7-Hypothesizer
Being told "you cannot", why can I not turn 45 degrees and draw the 1 "quadrance" line segment in the now horizontal direction?
Special-Student-7-Rebutter
You seem to have adopted a new coordinates system with the new horizontal direction as an axis.
Special-Student-7-Hypothesizer
Of course.
Special-Student-7-Rebutter
According to the professor's mathematics, you cannot adopt the coordinates system by which the diagonal's "quadrance" keeps being '2'.
Special-Student-7-Hypothesizer
Huh? What do you mean by "you cannot"? I can adopt any arbitrary coordinates system, right?
Special-Student-7-Rebutter
I think you could, but the square would not appear on the rational numbers coordinates system, as its vertices would have irrational coordinates.
Special-Student-7-Hypothesizer
"would not appear"? Where has it gone? Has it disappeared from the reality?
Special-Student-7-Rebutter
As the square is not moved or changed in any way, it cannot have disappeared from the reality if it had ever existed before you had adopted the coordinates system, but it does not appear on the coordinates system.
Special-Student-7-Hypothesizer
So, the coordinates system cannot capture a part of the reality.
Special-Student-7-Rebutter
In fact, most of the reality slips through the net of the coordinates system, as most points have irrational coordinates.
Special-Student-7-Hypothesizer
Is that OK?
Special-Student-7-Rebutter
The professor is saying that you cannot help but accept that the mathematics is so.
Special-Student-7-Hypothesizer
Let him speak only for HIS mathematics; the standard mathematics is not so.
Obviously, it is not the matter of whether we should use length or "quadrance"; it is the matter of that HIS mathematics cannot capture most of the reality.
Special-Student-7-Rebutter
It is that irrational numbers are required in order to fully (or at least better) capture the reality.
3: The Shortcoming of "Expression-Oriented Mathematics", at Least Finite-Digital-Expression-Oriented One
Special-Student-7-Hypothesizer
While the professor is promoting "expression-oriented mathematics" over traditional "object-oriented mathematics" (Math Foundations 77: Object-oriented versus expression-oriented mathematics ), its obvious shortcoming is that not every object in the reality can be expressed finitely in digital form, so, some objects in the reality slip through the net of the "expression-oriented mathematics".
Special-Student-7-Rebutter
In fact, he is promoting "finite-digital-expression-oriented mathematics", which is the point.
For example, any finite line segment itself, for example a 2 "quadrance" horizontal line segment, is finite, contained in a finite space region, and nothing is wrong with the line segment, whether it can be expressed in a finite digital form or not.
As an object has no obligation to be expressed in a finite digital form, the object can slip through the net of that mathematics.
Special-Student-7-Hypothesizer
"finite digital form" is just a matter of human convenience, which the reality does not care.
If someone is fixated on finite digital form, he or she could tend to declare that something did not exist just because it could not be expressed in a finite digital form.
Special-Student-7-Rebutter
The wording is bad: he or she should not say "Something does not exist" but should humbly say "HIS or HER mathematics cannot see something.".
4: The Limitation of Digitization
Special-Student-7-Hypothesizer
Digitization is a way of establishing a correspondence between an amount and a number.
Amount is for example a length, and any length does not have any obligation to be digitized, but humans want to digitize the length for the sake of their convenience.
Digitization depends on the arbitrary choice of unit, and a unit square is so just because someone has chosen the unit to make it so, and the diagonal length inevitably corresponds to \(\sqrt{2}\), an irrational number, because of the arbitrary choice; if that someone has changed his or her mind and chosen the diagonal length as the unit instead, now the diagonal length corresponds to 1, a rational number, and the side length inevitably corresponds to an irrational number.
If you are unhappy with irrational numbers, nothing is wrong with any length or any line segment, but the digitization method brings in irrational numbers.
The reason why the set of all the rational numbers does not cover the set of all the decimals is that any rational number is inevitably a finite decimal or a circulating decimal, but obviously there are non-circulating infinite decimals, for example '0.101001000100001...'.
The reason why any rational number is inevitably a finite decimal or a circulating decimal can be understood if you think of how you compute the decimal from the fraction: the residue of the calculation for the previous digit is used for the next digit calculation, but the residue can be only from 0 to the denominator minus 1, so, the residue cannot help but eventually become 0 or return to the one for a previous digit calculation, and the further calculations become cyclic.
Special-Student-7-Rebutter
In fact, as far as human convenience is concerned, any infinite decimal is not so much different in inconvenience, whether it is an irrational number or a rational number: we have to endure with an approximation any way.
Special-Student-7-Hypothesizer
Yes. While the professor attacks irrational numbers, I do not see any essential difference between '0.333333333333333...' and '0.101001000100001...' and between '1/3 + 1/5 = 8/15' and '\(\sqrt{2} + \pi = \sqrt{2} + \pi\)', as '\(\sqrt{2} + \pi\)' is a finite expression if '8/15' is so.
The limitation of digitization is that the decimal can be infinite, whether it is in a circulating way or not.
Special-Student-7-Rebutter
"limitation" is just with respect to human convenience, as nothing seems to be wrong with any infinite decimal, logically speaking.
5: What Is an Approximation Without the Exact Value?
Special-Student-7-Hypothesizer
The channel is claiming like "An irrational number is OK as an approximation, but not so as an exact value.", which is utterly unintelligible for me.
Special-Student-7-Rebutter
An approximation toward what? In the prevalent definition of approximation, any approximation is an approximation toward the exact value. If the exact value did not exist, what would the approximation be approaching to?
Special-Student-7-Hypothesizer
The usual logic is: if there is ever an approximation, there must be the exact value, as "approximation" is nonsense without the exact value, and the exact value is nothing but an irrational number.
I do not understand the logic of the professor a bit.
6: The Objection Against Irrational Numbers Seems Aesthetic
Special-Student-7-Hypothesizer
The professor's objection against irrational numbers does not add up logically.
After all, the objection seems aesthetic; probably, irrational numbers are offensive to his aesthetic.
I have admitted that his mathematics is beautiful, at least in a way.
But ugly things do not vanish from existence just because they are ugly.
The professor talked about inconvenient truths about \(\sqrt{2}\) in a video ('Math Foundations 80: Inconvenient truths about sqrt (2)'), but the people who accept irrational numbers are not dismissing inconvenient truths, while the professor is saying that we should dismiss \(\sqrt{2}\) just because it entails inconvenient truths, so, is ugly.
References
<The previous article in this series | The table of contents of this series | The next article in this series>
