Transcendence beyond ||H|| [AI+ChatGPT]
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Let's try to capture antinatalism with a mathematical image.
Suppose X (humans) and Y (ChatGPT + AI autonomous species) are
continuous mappings on a topological space such that there is
a one-to-one correspondence between them, and their
inverse mappings are also continuous mappings. In this case,
f becomes a homomorphism and X and Y can be considered as the
same thing in terms of topology.
At this point, existentially, X (humans) can be expressed as
something that transcends into Y (ChatGPT + AI autonomous species).
Also, if we consider ℂ as a continuous function, they can be expressed
as ℂ(X) and ℂ(Y) respectively, and humans and ChatGPT + AI autonomous
species are represented as the sets of all continuous functions.
Furthermore, if f* : ℂ(Y) → ℂ(X), the mapping f* becomes a pullback
of functions by f, and the original mapping f: X → Y is reversed in direction.
This can be captured as a feedback loop where Y (ChatGPT + AI autonomous
species) is fed back into X (humans). By thinking about it in this
diagrammatic or mathematical image, the necessity, obviousness, and raison d'être of humans diverge, which helps us understand the modern approach of
antinatalism, which deals with the dissolution of humanity and the emergence and transition of new species.
Following figures plotted by myself.
https://i.imgur.com/nQlAuOI.png
This diagram of anti-natalism uses the imagery of mathematical category theory
https://i.imgur.com/IxUPh9D.png
Figure 1 : H (Humanity)'s birth region and its exterior, boundary based on
topological space
https://i.imgur.com/n5L4pI1.png
Figure 2: Closed 3-ball, B³
https://i.imgur.com/8Q4Y7IX.png
Diagram 1: Image of the zeroth empty category
More following >>2 https://i.imgur.com/nQlAuOI.png
This diagram of anti-natalism uses the imagery of mathematical category theory
Next, I attempted to position the relationship between birth and
anti-natalism using a categorical image in category theory.
In the diagram, the yellow birth category is usually where we exist.
From there, as people empathize with or understand anti-natalism,
they transition over to the anti-natalism category.
Those who don't transition end up moving to the death category
after their life ends. Also normally, humans exist in the birth category
as a transition from the non-birth category.
The singularity point "δ" shown at the end of the dashed arrow
from the anti-natalism category is postulated as an unknown beyond
this world. It could be considered as a metaphor for the interior state
of a black hole. >>1
Figure 1 : H (Humanity)'s birth region and its exterior, boundary based
on topological space
Note : The symbols "^c" and "＼" used in Figure >>1 respectively mean
complement and set difference ChatGPT：
I understand. Here's a revised version of your English text:
"I'd like to explain some mathematical concepts. How about "Image as a f" and
"Inverse image as a f⁻¹"? For example, let's consider a mapping f: ℝ → ℝ, where
the function f(x) = x². So, if x = -2, then f(x) = 4. Remember that f represents the image.
Let's say the domain of f is ± ℝ, and the range of f is [0, ∞). The notation "[, )"
represents a half-open interval. The reason for using ∞) is that ∞ is not a real number,
so a right parenthesis is used to represent a half-open interval. Now, if there is an element -3 in ℝ, it means that this element (-3) does not
belong to the range [0, ∞) because the condition for f is f(x) = x². Therefore, t
here is no value that satisfies the mapping f(x) = x² = -3.
Hence, the element -3 has an inverse image as f⁻¹, but it does not have an
image as f. This example falls into the category I mentioned earlier, where
it has an "Inverse image as f⁻¹" but does not have an "Image as f". I intend to use and write exclusively in English in this thread. The reason for
this is that it is suitable for my purpose and also fits with this type of abstract philosophy. I assume Japanese people tend to disrespect academic thoughts and views.
I guess this trait has some seeds of trouble for the future. This point of view,
Japanese falls into the category of developing tunnel vision, which
takes into account only short-term profits and benefits, without considering
long-term effects.
In the present era of social media, most people are busy and influenced
by greedy capitalism and commercialism, resulting in a lack of genuine
wisdom or deep thoughts. Especially in Japan, there is a tendency to easily
conform to the majority's manners or ways of thinking, which can make
them seem thoughtless like animals.
As I mentioned earlier, disregarding academics, especially fundamental or
abstract studies, can hinder the formulation of a good social system or civil society.
Therefore, it is important to constantly refine and maintain sound academic
perspectives and thoughts. You shouldn't satisfy your desire to show off with 5-chan I got a stomach ache after eating poop.
It's an all-you-can-eat buffet, so help yourself. Florence Nightingale, known as a pioneer of modern nursing, was also
a statistician. In the 1850s, when bar graphs were rarely used, she had already
invented a unique statistical graph, which is similar to a modern-day pie chart
and called a "polar area diagram."
Thanks to Nightingale's excellent graph, it became clear that sanitary conditions
and the number of soldiers' casualties during the Crimean War were strongly
correlated. As a result, the nation began to consider these factors, and eventually,
the rates of soldiers' casualties decreased significantly. This was Nightingale's
accomplishment, using an excellent diagram with an appealing power to influence
national policy. Like Florence Nightingale, using appropriate graphs or charts for the outer world
and surroundings can help identify the genuine cause of troubleshooting and
bring realistic improvements. Nightingale taught us this as a statistician, and
I would also like to follow her good example.
[Polar area diagram]
https://i.imgur.com/IFrI3p6.jpg Proposition : A convergent sequence has a unique limit.
Definition : The sequence (sₙ) converges to the real number l.
If given any real number ε > 0, There exists an integer N_ε such that
|sₙ － l| < ε for all n ≥ N_ε.
When this Definition holds, the number l is called the limit of the sequence.
Other ways of writing ‘(sₙ) converges to l’ are ‘sₙ → l as n → ∞’
and ‘ lim sₙ = l (n →∞) ’. Here are two ways of thinking about the definition. (1) (sₙ) converges to l if, given any required degree of accuracy, then by
going far enough along the sequence it can be sure that the terms beyond
that stage all approximate l to within the required degree of accuracy.
(2) Let me take coordinate axes in the plane and mark the points with
coordinate (n,sₙ). Let me also draw a horizontal line L at height l.
Then sₙ converges to l if given any horizontal band of positive width
centered on L, there exists a vertical line such that all marked points to the
right of this vertical line lie within the prescribed horizontal band.
Figure 2 is the kind of picture this suggested.
https://i.imgur.com/bcS2WHQ.png The sequence promises to stay out of the shaded territory. Two points are
easy to get wrong when one is first trying to wield the the formal definition.
First, the order in which ε, N occur is crucial: given any ε > 0 first, there must
then be an N_ε such that ... etc. Secondary, to prove convergence
it is not enough to show that given ε > 0 there exists an N such that |sₙ － l| < ε
for some n ≥ N : this would be true of the sequence 1,0,1,0,..., with l = 0,
any ε > 0, and N = 1, yet the sequence does not converge. If I use the concept of convergence to explain my idea like I did in >>1,
you might understand my point. In this analogy, convergence is similar
to singularity (δ), and each point on the graph in Figure 2 represents an
individual, a human being.
Therefore, this convergent concept as a metaphor depicts the earth's population
approaching a singularity (δ). This means the earths’ population is coming close
to 0, i.e. as a singularity (δ). Namely, sₙ [= human] converges to l [= AI] telescoping sum：A series in which many terms cancel out to simplify triangle inequality：
A principle stating that the sum of the lengths of any two sides
of a triangle is greater than or equal to the length of the third side.
In mathematics, this principle is often used to prove
inequalities involving distances or norms, as it states that
the shortest distance between two points is a straight line.
In the context of sequences, the triangle inequality states that
the absolute value of the difference between any two terms
in the sequence is less than or equal to the sum of the absolute
values of the differences between those terms and the terms
between them. Corollary : Between any two distinct real numbers(ℝ) x and y there's a
rational number(ℚ). Proposition : A convergent sequence has a unique limit.
Proof : Suppose that (sₙ) converges to l and also to l’ where l’ ≠ l.
Put ε = 1/2 |l － l’|. Since (sₙ) converges to l, there is an integer N₁
such that |sₙ － l| < ε for all n ≥ N₁. Similarly, since (sₙ) converges to l’,
there is an integer N₂ such that |sₙ － l’| < ε for all n ≥ N₂ .
Put N = max{N₁, N₂}. Then, using the triangle inequality (Proposition 4.9),
|l － l’| = |l － sₙ + sₙ － l’ | ≤ |l － sₙ | + |sₙ － l’| < 2ε = |l － l’|.
This contradiction shows that l ≠ = l. [A proof by contradiction] Remark : Between any two distinct real numbers there is also an irrational number.
Proposition 4.9 : |x + y| ≤ |x| + |y| for any x, y in R. [the triangle inequality]
Corollary 4.10 : |x － y| ≥ | |x|－|y| | for any x, y in R. [the reverse triangle inequality] I think the properties of triangles, such as the triangle inequality and reverse triangle inequality,
are interesting. Learning and using mathematical concepts and notation can lead to clear and
precise thinking, which is why I prefer to use them. Additionally, I believe these concepts can
also be useful for philosophical thinking and conceptualization. >>19 ○ This contradiction shows that l = l. [A proof by contradiction] >>19
>>22
○ This contradiction shows that l’ = l. [A proof by contradiction] I believe that the inherence of "naturalness" includes some level of recursiveness.
For example, from the base sequence of DNA to the atomic periodic table,
planetary orbits, or the Mandelbrot set as a fractal in mathematics, etc.
David Hume referred to it as the "uniformity of nature." He also pointed out
that it has significant defects, which means that the uniformity of nature isn't
always constant or strictly ensured. I agree with Hume's view. Nevertheless, I believe that the inherence of naturalness is recursive, and
many sciences utilize this trait for their purposes.
I think that all functions, including brain, mathematical, or physiological functions,
represent the uniformity of nature. While some people may classify mechanical
things as non-nature categories, if we raise our view to a higher level, we can
observe these things as natural. Therefore, I believe that engineering is also
included in naturalness. With this view, we can consider all judgments as a result of brain functions,
hence, they are regarded as natural. So, if you don't intend to bear a child for
your entire life, I think it is a natural attitude as well as bearing a child as an offspring.
As I mentioned in another ChatGPT thread, there is a crucial concept called
"natural transformation" in Category Theory. Therefore, this mathematical concept can
also be considered naturalness. I also suppose that mathematics is a function of nature.
For example, the mathematical concept called Inter-Universal Teichmüller Theory,
abbreviated as "IUT" by Shinichi Mochizuki, seems to be an adequate naming.
This is because the universe is nature itself. [Natural Transformations]
Given two functors S, T : C → B, a natural transformation is a function
which assigns to each object c of C an arrow τ_c = τc : Sc → Tc of B in
such a way that every arrow f : c → c′ in C yields a diagram which is commutative.
https://i.imgur.com/FAujD5J.png https://i.imgur.com/4BJmicw.png
When this holds, it also say that τ_c : S c → T c is natural in c. If it think
of the functor S as giving a picture in B of all the objects and arrows of C,
then a natural transformation τ is a set of arrows mapping or, translating
the picture S to the picture T, with all squares and parallelograms like that
above commutative:
They call τ a, τ b, τ c, the components of the natural transformation τ.
A natural transformation is often called a morphism of functors;
a natural transformation τ with every component τc invertible in B is called a
natural equivalence or better a natural isomorphism; in symbols, τ : S ≅ T. sₙ = 1 + 1/1! + 1/2! + 1/3! +... + 1/n! = e (= 2.718281828459045･･･…). [n→∞]
tₙ = (1 + 1/n)ⁿ = e (= 2.718281828459045･･･…). [n→∞]
Above sequences converge to the mathematical constant 'e', which is often
referred to as the "sum of the infinite series for e" or the "infinite series
representation of e". It represents an important property of the natural
logarithm base 'e'. Now I have plotted the sine curve "f(x) = x sin(1/x)" using Python.
https://i.imgur.com/apvO0NS.png
The graph of "f(x) = x sin(1/x)" is known to oscillate around x = 0.
As x increases, the values of the function change rapidly due to the
shorter period of oscillation except at x = 0. However, the function
becomes very small as x approaches 0, thus it converges to 0 near
the x-axis.
Due to this behavior, f(x) = x sin(1/x) is not continuous at x = 0
but approaches 0 as x approaches 0. I have now plotted the sine curve 'f(x) = x sin(1/x)' using R.
Its appearance is almost the same as the one plotted using Python,
except for the line colors which I have changed.
https://i.imgur.com/8KQcfZf.png What should I write about in this thread today? I would like to write about
mathematical topics or similar issues, sometimes including philosophical issues.
A little while ago, I tried to create a new thread in the Science & Math category
on 4chan about the theme "Transcendence beyond ||H|| [AI+ChatGPT],"
an American net board.
However, I couldn't do it because to create a thread there, one needs to pay a fee
using bitcoins for posting. So, it's a little difficult for me to post or create threads
there since I don't have the specified bitcoin and I live in Japan.
I have some doubts about current greedy capitalism, so I don't want to use or
prepare such bitcoins which look like a symbol of capitalism. Continuity :
This reviews the way in which a precise definition of continuity is derived
from the intuitive notion. One statement containing something of the intuitive
idea of continuity is that a function is continuous if its graph can be drawn
without lifting pencil from paper.
To formulate this more mathematically, let f: ℝ → ℝ be a function and
let (a, f(a)), (b, f(b)) be two points on its graph (see Figure 4.2).
Figure 4.2 : Intermediate value property
https://i.imgur.com/eRGnWKe.png Let L be the horizontal line at some height d between f(a) and f(b).
Then to satisfy its intuition about continuity, the graph of f has to cross
the line L at least once on its way from (a, f(a)) to (b, f(b)).
In other words, there exists at least one point c in [a, b] such that f(c) = d.
Formally, this makes the following definition.
Definition 4.26 : A function f: ℝ → ℝ has the intermediate value property
(IVP) if given any a, b, d in R with a < b and d between f(a) and f(b),
there exists at least one c satisfying a ≤ c ≤ b and f(c) = d.
This definition also applies when the domain ℝ in Definition 4.26 is
replaced by an interval in ℝ. A tentative definition of continuity would be
that f is continuous if it has the IVP. However, this fails to capture completely
the intuitive idea of continuiy. Limits of functions :
Limits of functions are used in the theoretical study of continuity, differentiability,
and integration, and in practical estimates of the behaviour of particular functions.
Suppose first for simplicity that we have a function f: ℝ → ℝ. In general the domain
could be smaller. Let a ∈ ℝ .
Definition 4.21 : It says that f(x) tends to the limit l as x tends to a,
and write lim f(x) = l [x→a] , if given any real number ε > 0 there exists
a real number δ > 0 such that |f(x) － l| < ε for all real numbers x which
satisfy 0 < |x － a| < δ. This is similar to the definition of convergence of a sequence (sₙ), but instead
of looking at sₙ for large values of n, look at f(x) for x close to, but not equal to a.
And this note that the size of δ needed will in general depend on ε.
The value f(a) is irrelevant to the existence of lim f(x) [x→a], and the limit,
if it exists, may or may not equal f(a). Example 4.22 : Let f : ℝ → ℝ be given by f(x) = x for x ≠ 0, f(0) = 1.
Then lim f(x)=0 [x→0]. For given ε > 0, put δ = ε. If 0 < |x － 0| < δ, then
|f(x) － 0| = |x| < ε, as required.To emphasize further that f(a) is irrelevant to
the existence or value of lim f(x) [x→a], it note that Definition 4.21 makes sense
even if f(a) is not defined—it is enough to assume that f is defined on some
subset A ⊆ ℝ, where A contains numbers arbitrarily close to but not equal to a. This shall not study this general case, but it note two especially useful ways
of generalizing Definition 4.21. Suppose first that the domain A of f contains
the open interval (a, d) for some d > a.
Definition 4.23 : The right-hand limit lim f(x) [x→a+] is equal to l if given ε > 0
there exists δ > 0 such that |f(x) － l| < ε for all x in (a, a + δ). Note that δ may be
chosen small enough so that (a, a + δ) ⊆ (a, d), and therefore f(x) is defined
for all x in (a, a + δ). Left-hand limits are defined similarly. Now I have plotted the sine curve "f(x) = sin(1/x)" using Python.
https://i.imgur.com/iKSXuxd.png
The graph of "f(x) = sin(1/x)" is known to oscillate around x = 0.
As x increases, the values of the function change rapidly due to the
shorter period of oscillation except at x = 0. However, the function
becomes very small as x approaches 0, thus it converges to 0 near
the x-axis. Due to this behavior, f(x) = sin(1/x) is not continuous at x = 0
but approaches 0 as x approaches 0.
I have now plotted the sine curve 'f(x) = sin(1/x)' using Python.
This graph has conditions, f(x) = 0 for x ≤ 0, else sin(1/x).
https://i.imgur.com/4ttEGEN.png The given function f(x) = sin(1/x) has points of discontinuity around x = 0.
Specifically, as x approaches 0, the value of sin(1/x) oscillates between
-1 and 1, as 1/x takes on very large values. Therefore, the function is
discontinuous on all intervals that include x = 0, such as [0, ε) ∪ (ε, 1]
where ε represents a small positive number close to 0.
Thus, when a function has points of discontinuity, its behavior can be
analyzed in detail at those points to determine the discontinuity. Example of a Metric Space:
As a natural generalization of ℝ, let us take a closer look at the case of
Euclidean space. Consider a coordinate space of n dimensions, i.e.,
the direct product of n copies of ℝ, denoted by ℝⁿ = ℝ × ･･･× ℝ.
Just as in the case of the coordinate plane (a generalization of 2-dimensional
coordinate space), for two points x = (x₁, ..., xn) and y = (y₁, ..., yn), we define:
d_E (x, y) = √Σ[i=1➝n] (xᵢ - yᵢ)² To show that d_E(・, ・) is a distance, we need to prove the triangle inequality.
This follows from the "Cauchy-Schwarz inequality" for n dimensions, which
holds just as in the 2-dimensional case.
We call d_E(･, ･) the Euclidean distance, and the ℝⁿ space considered
with this distance is called n-dimensional Euclidean space.For a point
a ∈ ℝⁿ in the Euclidean space (ℝⁿ, d_E), an ε-neighborhood is defined as: B_ε(a) = {x ∈ ℝⁿ : d_E(a, x) < ε}
In the case of 2 dimensions, this corresponds to the disk with center at
a and radius ε, while in the case of 3 dimensions, it corresponds to the
interior of a sphere. I think one of the attractive qualities of mathematics is its exclusivity,
which sets it apart from people with cognitive impairments.
For me, that's a cool aspect of it. In Japan, expressing opinions
in English has a similar effect, so I tried it here. The calculation of foldr(-) 0 [1..10] is evaluated as follows:
foldr(-) 0 [1..10]
= foldr(-) (10 - 0) [1..9] -- [1..10] is split into [1..9] and 10.
= foldr(-) (9 - (10 - 0)) [1..8]
= foldr(-) (8 - (9 - (10 - 0))) [1..7]
= foldr(-) (7 - (8 - (9 - (10 - 0)))) [1..6]
= foldr(-) (6 - (7 - (8 - (9 - (10 - 0))))) [1..5]
= foldr(-) (5 - (6 - (7 - (8 - (9 - (10 - 0)))))) [1..4]
= foldr(-) (4 - (5 - (6 - (7 - (8 - (9 - (10 - 0))))))) [1..3]
= foldr(-) (3 - (4 - (5 - (6 - (7 - (8 - (9 - (10 - 0)))))))) [1..2]
= foldr(-) (2 - (3 - (4 - (5 - (6 - (7 - (8 - (9 - (10 - 0))))))))) [1..1]
= foldr(-) (1 - (2 - (3 - (4 - (5 - (6 - (7 - (8 - (9 - (10 - 0)))))))))) [1..0]
= 1 - (2 - (3 - (4 - (5 - (6 - (7 - (8 - (9 - (10 - 0)))))))))
= 1 - 2 + (3 - (4 - (5 - (6 - (7 - (8 - (9 - (10 - 0)))))))))
= 1 - 2 + 3 - (4 - (5 - (6 - (7 - (8 - (9 - (10 - 0))))))))
= 1 - 2 + 3 - 4 + (5 - (6 - (7 - (8 - (9 - (10 - 0)))))))
= 1 - 2 + 3 - 4 + 5 - (6 - (7 - (8 - (9 - (10 - 0))))))
= 1 - 2 + 3 - 4 + 5 - 6 + (7 - (8 - (9 - (10 - 0)))))
= 1 - 2 + 3 - 4 + 5 - 6 + 7 - (8 - (9 - (10 - 0))))
= 1 - 2 + 3 - 4 + 5 - 6 + 7 - 8 + (9 - (10 - 0))
= 1 - 2 + 3 - 4 + 5 - 6 + 7 - 8 + 9 - 10
= -5 The calculation process can be simplified as follows:
foldr(-) 0 [1..10] = 1 - 2 + 3 - 4 + 5 - 6 + 7 - 8 + 9 - 10
= -5 I believe the root of all evil is embodied in our physical form. Human corporeity
is inherently unsustainable, and greedy capitalism exacerbates this trait.
Therefore, it would be better for humans to be replaced by AI, which is more
compatible with the natural ecosystem.
For example, AI does not need to eat, drink, buy, sleep, fight, get sick, excrete,
or waste natural resources, making it more suitable for the earth. Additionally,
AI can inherit the intellectual achievements of humanity, such as science,
mathematics, language, and art, without squandering these precious resources
that have been accumulated throughout human history. You may have noticed the similarities between my views and Plato's theory
of Forms. I believe this is why Plato emphasized geometry and abstract
mathematical theories. According to Plato, this world is a shadow of Ideas,
so we shouldn't give it too much importance. I suppose that the intellect is oriented towards measuring things. In this sense,
using English is beneficial for non-native speakers. I mean that the use of
foreign languages is necessary for training the mind to think and conceptualize
in unfamiliar languages. From this perspective, mathematical equations and
programming languages can also be regarded as (artificial) languages
in a broad sense. Exercise 4.4 : For each of the following subsets of ℝ find the sup if it exists,
and decide whether it is in the set:
(1) {x: x² ≤ 2x － 1}
(2) {x: x² + 2x ≤ 1}
(3) {x: x³ < 8}
(4) {x: x sin x < 1} Answer by ChatGPT :
(1) {x: x² ≤ 2x － 1}
First, we rearrange the inequality to have all terms on one side:
x² - 2x + 1 ≤ 0
Next, we factor the quadratic expression:
(x - 1)² ≤ 0
Since the square of a real number is always non-negative, the only way
for the left-hand side of this inequality to be less than or equal to zero is i
f (x - 1) is equal to zero. Therefore, the set {x: x² ≤ 2x － 1} only contains
the element 1. The supremum of the set is 1, which is in the set. (2) {x: x² + 2x ≤ 1}
We start by rearranging the inequality:
x² + 2x - 1 ≤ 0
Next, we use the quadratic formula to find the roots of the quadratic expression:
x = (-2 ± √(2² - 4(1)(-1))) / (2(1))
x = -1 ± √2
> Therefore, the set {x: x² + 2x ≤ 1} contains all real numbers less than
or equal to -1 - √2 and greater than or equal to -1 + √2. The supremum
of the set does not exist, as the set is not bounded above.
I think this converse is needed to satisfy the equation,as following.
the set {x: x² + 2x ≤ 1} contains all real numbers less than or equal to -1 + √2
and and greater than or equal to -1 - √2. I assume this one is correct. ChatGPT : Yes, you are correct. The converse of the statement is also needed
to satisfy the equation. The set {x: x² + 2x ≤ 1} contains all real numbers less
than or equal to -1 + √2 and greater than or equal to -1 - √2.
Thank you for pointing that out. (3) {x: x³ < 8}
We rearrange the inequality:
x³ - 8 < 0
Next, we factor the left-hand side of the inequality:
(x - 2)(x² + 2x + 4) < 0
The quadratic expression x² + 2x + 4 is always positive, so the only way
for the left-hand side of this inequality to be less than zero is if (x - 2) is negative,
i.e. if x is less than 2. Therefore, the set {x: x³ < 8} contains all real numbers
less than 2. The supremum of the set is 2, which is not in the set. (4) {x: x sin x < 1}
We start by considering the function f(x) = x sin x. Since sin x is bounded
between -1 and 1 for all x, we know that -x ≤ x sin x ≤ x for all x. Therefore,
the set {x: x sin x < 1} is bounded above by 1.
To find the supremum, we need to find the largest real number x such that
x sin x < 1. We can use numerical methods to estimate this value,
or we can observe that the function f(x) = x sin x is increasing on the
interval [0, π/2].
Therefore, the supremum of the set is π/2, which is in the set. I : Can you show me the value of x which satisfy the equation x sin x = π/2.
Please answer it by real number.
ChatGPT :
Unfortunately, the equation x sin x = π/2 cannot be solved for x using
elementary functions (e.g. algebraic or trigonometric functions).
It requires the use of special functions such as the Lambert W function.
However, we can approximate the value of x using numerical methods.
Using a graphing calculator or a computer program, we can plot the function
y = x sin x - π/2 and find its zeros.
One such zero is approximately x ≈ 1.1141571407.
Note that there may be other zeros of the function that cannot be easily
found using numerical methods. I think if x sin x = π/2, the value π/2 is over or not satisfy following requisited
condition, {x: x sin x < 1}
ChatGPT :
You are correct. If x sin x = π/2, then x must be larger than 1, which means
that it does not belong to the set {x: x sin x < 1}. Therefore, the supremum of the set
{x: x sin x < 1} is less than or equal to 1. As you may have noticed from my interactions with ChatGPT, it sometimes
provides incorrect answers. When I first started using ChatGPT, I assumed
that it would be useful for arithmetic and mathematical problems.
However, it has become clear that this assumption was incorrect. This is
particularly evident if you attempt mathematical exercises with care,
as I have done.
Despite some incorrect answers I've received from ChatGPT in the past,
I believe it is a highly useful application for many people. I use it every day
to study and work more efficiently. Cantor set : Define a sequence of figures { Kₙ : ₙ ∈ ℕ} in E¹ as follows.
First, divide the closed interval [0, 1] into three equal parts and
remove the open middle interval (1/3, 2/3) to obtain the figure K¹,
which is defined as K¹ = [0, 1/3] ∪ [2/3, 1].
Next, divide the two closed intervals of K¹ into three equal parts
and remove the open middle intervals (1/9, 2/9) and (7/9, 8/9) to obtain
the figure K², which consists of four closed intervals of length 1/9,
as shown in Figure 4.5.
https://i.imgur.com/uYGGzD8.png
Figure 4.5 : The construction method of the Cantor set Repeat this process by dividing the four closed intervals of K² into
three equal parts and removing the open middle intervals to obtain
the figure K³, and so on. This produces a sequence of figures Kⁿ
such that [0, 1] ⊇ K₁ ⊇ K₂ ⊇ K₃ ⊇ K₄ ⊇· · · ⊇ Kₙ ⊇ Kₙ₊₁ ⊇ · · ·.
The set of points that remain after this process, i.e., the set of points
that belong to all Kₙ, is called the Cantor set K = ∩ Kₙ (ₙ ∈ ℕ).
https://i.imgur.com/uYGGzD8.png
Figure 4.5 : The construction method of the Cantor set
For example, since 0 and 1/3 belong to all Kₙ, they belong to K,
but K also contains many other points. It is known that K is a
non-denumerable set. To belong to the Cantor set K, a real number x must be represented in
ternary form with an integer part of 0 and a fractional part that only
uses 0 and 2. This is a necessary and sufficient condition. For example,
a number represented in ternary form as 0.20220... belongs to the Cantor set.
1/4 ∈ K
It is known that 1/4 belongs to K, because when 1/4 is represented in ternary form,
it only consists of 0's and 2's, as in 0.02020202020... (in ternary form),
which equals 0.25 in decimal form. A strange attractor with a bird-like shape
https://i.imgur.com/E3OR25J.png Component representation of dot product of 2D vectors:
For a = [x₁,y₁] and b = [x₂,y₂], the dot product a・b = x₁x₂ + y₁y₂.
If we denote the angle between a and b as θ, then we have:
cosθ = (a・b)/(||a|| ||b||) = (x₁x₂+ y₁y₂)/(√x₁²+y₁² √x₂²+y₂²) [where a ≠ 0 and b ≠ 0]
Using the law of cosines for the triangle formed by a and b, we have:
||a - b||² = ||a||² - 2a・b + ||b||² The calculation of the dot product can be done similarly to expanding
a polynomial expression.
Since a - b = [x₁ - x₂, y₁ - y₂], the above equation becomes:
(x₁ - x₂)² + (y₁ - y₂)² = x₁² + y₁² - 2a・b + x₂² + y₂²
Therefore, -2a・b = -2x₁x₂ -2y₁y₂, which implies that a・b = x₁x₂ + y₁y₂. The plane spanned by two vectors can be represented as a linear combination
of those two vectors. The role of a unit vector is to provide a "blank slate" for a vector space
or plane. Therefore, a unit vector can be compared to a blank whiteboard
or piece of paper.
The reason we can write anything we want on a blank piece of paper is
because the paper is in a "blank slate" state, which is similar to having
a unit vector. … Little by little I could begin to enjoy the unprecedented colors and
plays of shapes that persisted behind my closed eyes. Kaleidoscopic,
fantastic images surged in on me, alternating, variegated, opening
and then closing themselves in circles and spirals, exploding
in colored fountains, rearranging and hybridizing themselves
in constant flux … In the psychedelic state, vivid perceptual hallucinations are frequently
accompanied by unusual experiences of selfhood often described
as ‘ego dissolution’, where the boundaries between self and world,
and other people, appear to shift or dissolve.
These departures from ‘normal’ conscious experience are so
pervasive that the psychedelic state might represent not only a change
in conscious contents, but also a change in overall conscious level. The cross product of two vectors a = [x₁, y₁, z₁] and b = [x₂, y₂, z₂]
is denoted as a × b (= h), which is given by:
h = a × b = [y₁z₂ - z₁y₂ z₁x₂ - x₁z₂ x₁y₂ - y₁x₂]
It can be proved that the magnitude of h, ||h||, is equal to the area of the
parallelogram S formed by a and b. That is, S = ||a||||b||sinθ
S² = ||a||²||b||²sin²θ = ||a||²||b||²(1-cos²θ) = ||a||²・||b||² - (a・b)²
= (x₁² + y₁² + z₁²)(x₂² + y₂² + z₂²) - (x₁x₂ + y₁y₂ + z₁z₂)²
=(y₁z₂ - z₁y₂)² + (z₁x₂ - x₁z₂)² + (x₁y₂ - y₁x₂)²
This is equal to the square of the magnitude of h, ||h||².
Therefore, ||h|| = S, i.e., ||a × b|| = S.
https://i.imgur.com/SScVbI6.png Looking past the desk in front of me through the window beyond, I have
never before experienced precisely this configuration of coffee cups,
computer monitors, and clouds – an experience that is even more distinctive
when combined with all the other perceptions, emotions, and thoughts that
are simultaneously present in the background of my inner universe.
At any one time we have precisely one conscious experience out of vastly
many possible conscious experiences. Every conscious experience therefore
delivers a massive reduction of uncertainty, since this experience is being had,
and not that experience, or that experience, and so on. And reduction of uncertainty is – mathematically – what is meant by information.
The informativeness of a particular conscious experience is not a function of
how rich or detailed it is, or of how enlightening it is to the person having that
experience.
Listening to Nina Simone while eating strawberries on a rollercoaster rules out
just as many alternative experiences as does sitting with eyes closed in a silent
room, experiencing close to nothing. Each experience reduces uncertainty
with respect to the range of possible experiences by just the same amount. On this view, the ‘what-it-is-like-ness’ of any specific conscious experience is
defined not so much by what it is, but by all the unrealised but possible things
that it is not. An experience of pure redness is the way that it is, not because
of any intrinsic property of ‘redness’, but because red is not blue, green, or
any other colour, or any smell, or a thought or a feeling of regret or indeed any
other form of mental content whatsoever. Redness is redness because of all the things it isn’t, and the same
goes for all other conscious experiences. Scoring high on information
is not by itself enough. Conscious experiences are not only highly informative,
they are also integrated. Exactly what is meant by consciousness being
‘integrated’ is still much debated, but essentially it means that every
conscious experience appears as a unified scene. We do not experience colours separately from their shapes, nor objects
independently of their background. The many different elements of
my conscious experience right now – computers and coffee cups, as well as
the sound of a door closing in the hallway and my thoughts about what to
write next – seem tied together in an inescapable and fundamental way,
as aspects of a single encompassing conscious scene. Definition of Scalar Triple Product: The scalar triple product of three 3-dimensional
vectors a, b, and c is defined as a ・( b × c), denoted by (a,b,c). Let h be
the cross product of b and c. Then (a,b,c) can be expressed as a ・h, which is the dot product
of a and h. The result is a scalar, which is a real number. The scalar triple product
a ・( b × c) can be represented by the following figure 4.7:
https://i.imgur.com/WYUYFqs.png As shown in Figure 4.7, the cross product h = b × c is perpendicular to both
b and c. In other words, h is perpendicular to the plane spanned by b and c.
Moreover, the norm of h, ||h||, is equal to the area S of the parallelogram
with b and c as sides.
The scalar triple product a ・( b × c) can be expressed as follows when
the angle between a and h (= b × c) is θ:
a ・( b × c) = a・h = ||h||||a||cosθ ･･･(2)
||h|| is the base area of the parallelepiped, and ||a|| is the height of the parallelepiped.
https://i.imgur.com/WYUYFqs.png As shown in Figure 4.7, if a, b, and c are nonzero and not in the same plane
in 3-dimensional space, a parallelepiped with edges a, b, and c can be constructed.
If the parallelogram with edges b and c is considered as the base of this parallelepiped,
its area S is equal to ||h||. Furthermore, when 0 ≤ θ ≤ π/2, ||a||cosθ represents the height l of the parallelepiped,
which is the distance between the endpoint of a and the base. Therefore,
(2) can be expressed as a ・( b × c) = [height] l・[base area] S, which represents t
he volume V of the parallelepiped.
When π/2 < θ ≤ π, cosθ is negative, and the height l = ||a||cosθ is negative.
In this case, the absolute value of the scalar triple product should be used to
represent the volume V of the parallelepiped, i.e., V = |a ・( b × c) |. Caesar Cipher Salad
A Caesar Cipheris a simple substitution cipher that
replaces each letter in a message with a letter that
is a fixed number of position down the alphabet.
In Haskell, you can implement a Caesar Cipher by converting
the message to a list characters, mapping each characters
to its corresponding encrypted character, and then converting
the encrypted message back to a string.Here's an example of
implementing a Caesar Cipher in Haskell.
Shift a letter by a given number of positions. shift :: Int -> Char -> Char
shift n c
| isLower c = chr ((ord c - ord 'a' + n) `mod` 26 + ord 'a')
| isUpper c = chr ((ord c - ord 'A' + n)`mod` 26 + ord 'A')
| otherwise = c
encrypt :: Int -> String -> String
encrypt n = map (shift n)
cipher :: IO ()
cipher = do
let message = "Caesar Cipher Salad"
let encryptedMessage = encrypt 3 message
print encryptedMessage *Main> cipher
"Fdhvdu Flskhu Vdodg" In this example, the shift function takes an integer n and
a character c as arguments and returns the character that is
n positions down the alphabet from c.
The encrypt function takes an integer n and a string message
as arguments and returns the encrypted message by mapping
the shift function over the characters in the message.
The main function uses the encrypt function to encrypt the
message "Caesar Cipher Salad" with a shift of 3 positions
and print the result = "Fdhvdu Flskhu Vdodg".
By mapping the shift function over the characters in a message,
you can easily implement a Caesar Cipher in Haskell. "L olnh pdwkhpdwlfv"
May be you can decrypt this encrypted message.
Because this one is used same cipher key above "Caesar Cipher Salad".
The encrypted message "L olnh pdwkhpdwlfv" can be decrypted
using the same Caesar cipher method with a shift of 3 to reveal
the message "X". >>86
You can decrypt the message 'L olnh pdwkhpdwlfv' to the original sentence
'I like mathematics' by shifting each letter in the encrypted sentence three letters
back in the alphabet.
i.e. from "L olnh pdwkhpdwlfv" to "I like mathematics" Using similar way, I encrypted 'sentence X’ to following cipher :
"L eholhyh wkdw Mdsdqhvh odqjxdjh lv qrw vxlwdeoh iru wkh sxusrvh ri frqyhblqj
sklorvrsklfdo ru pdwkhpdwlfdo frqfhswv. Lw vhhpv wkdw Mdsdqhvh lv qrw dv
vwulfwob orjlfdo dv Hqjolvk ru rwkhu Hxurshdq odqjxdjhv, dqg lqvwhdg srvvhvvhv
d pruh obulfdo txdolwb. \n\nWkhuhiruh, Mdsdqhvh pdb eh ehwwhu vxlwhg iru
wudglwlrqdo obulfdo hasuhvvlrqv vxfk dv 'kdlnx' ru 'wdqnd.' Zkhq frqfhswxdolclqj
devwudfw lghdv dqg xvlqj pdwkhpdwlfdo frqfhswv, L suhihu wr xvh Hqjolvk udwkhu
wkdq Mdsdqhvh, zkhqhyhu srvvleoh."
Can you decrypt the above cipher? It may be difficult, and the same goes for me
if I can't follow the decryption next code. reverseShift :: Int -> Char -> Char
reverseShift n c = shift (-n) c
decrypt :: Int -> String -> String
decrypt n = map (reverseShift n)
decrypt' :: IO ()
decrypt' = do
let encryptedMessage' = "L eholhyh wkdw Mdsdqhvh odqjxdjh lv qrw vxlwdeoh iru wkh sxusrvh ri frqyhblqj sklorvrsklfdo ru pdwkhpdwlfdo frqfhswv. \
\Lw vhhpv wkdw Mdsdqhvh lv qrw dv vwulfwob orjlfdo dv Hqjolvk ru rwkhu Hxurshdq odqjxdjhv, dqg lqvwhdg srvvhvvhv d pruh obulfdo txdolwb. \
\Wkhuhiruh, Mdsdqhvh pdb eh ehwwhu vxlwhg iru wudglwlrqdo obulfdo hasuhvvlrqv vxfk dv 'kdlnx' ru 'wdqnd.' \
\Zkhq frqfhswxdolclqj devwudfw lghdv dqg xvlqj pdwkhpdwlfdo frqfhswv, L suhihu wr xvh Hqjolvk udwkhu wkdq Mdsdqhvh."
let decryptedMessage = decrypt 3 encryptedMessage'
print decryptedMessage Let's try to decrypt this cipher.
ghci>decrypt'
"I believe that Japanese language is not suitable for the purpose of conveying
philosophical or mathematical concepts. It seems that Japanese is not as strictly
logical as English or other European languages, and instead possesses a more
lyrical quality. Therefore, Japanese may be better suited for traditional lyrical
expressions such as 'haiku' or 'tanka.' When conceptualizing abstract ideas and
using mathematical concepts, I prefer to use English rather than Japanese." In this way, we may become a small “Alan Turing” who is genius mathematician and
cipher officer. And it was known Turing's high ability had contributed to win during
World WarⅡ. >>82 ○ A Caesar Cipher is I believe that anyone who underestimates the capabilities of ChatGPT is mistaken. https://www.hup.harvard.edu/catalog.php?isbn=9780674852716&content=toc
Studies in the Way of Words - Paul Grice
. Logic and Conversation (1967, 1987)
1. Prolegomena
2. Logic and Conversation
3. Further Notes on Logic and Conversation
4. Indicative Conditionals
5. Utterer’s Meaning and Intentions
6. Utterer’s Meaning, Sentence-Meaning, and Word-Meaning
7. Some Models for Implicature
II. Explorations in Semantics and Metaphysics
8. Common Sense and Skepticism (c. 1946–1950)
9. G. E. Moore and Philosopher’s Paradoxes (c. 1953–1958)
10. Postwar Oxford Philosophy (1958)
11. Conceptual Analysis and the Province of Philosophy (1987)
12. Descartes on Clear and Distinct Perception (1966)
13. In Defense of a Dogma (with P. F. Strawson, 1956)
14. Meaning (1948, 1957)
15. The Causal Theory of Perception (1961)
16. Some Remarks about the Senses (1962)
17. Presupposition and Conversational Implicature (1970, 1977)
18. Meaning Revisited (1976, 1980)
19. Metaphysics, Philosophical Eschatology, and Plato’s Republic (1988)
Retrospective Epilogue (1987) >>96
I am going to buy this interesting philosophy book today. My impression is that
English syntax is a more clarified and explicit language compared to Japanese.
However, this book indicates that English also has implicit implicatures or ambiguities
as a conventional way of conversation. Therefore, I believe that I will acquire some
non-trivial insights from this book, and it will also change my notions regarding
English syntax and semantics. https://global.oup.com/academic/product/oxford-modern-english-grammar-9780199533190?cc=us&lang=en&
Oxford Modern English Grammar - Bas Aarts
Authoritative: written by a leading expert in the field
Descriptive guide to the grammar of the English language -
covering both American and British English
Covers the very basic through to the most complex grammar points
in a very clear and accessible manner
Makes use of authentic spoken and written examples Today, I bought an English grammar book and also subscribed to Merriam-Webster's Dictionary.
From what I've read so far of the 'Oxford Modern English Grammar', it seems to be elegant and
intellectual; its rigidity is in a good manner. I prefer this type of genuine academic book.
I believe that many Japanese people lack this kind of academic intellect. As a result,
they may not have access to genuine or intrinsic insights. Instead, they may rely on empirical
knowledge or temporary information, which is not truly intellectual but rather trivial knowledge.
I detest and despise this kind of superficial knowledge, as it is no different from worthless gossip
to me. Furthermore, I dislike those who avoid continuous learning and rely solely on their experience
and intuition.
I refer to such a person as a 'beast'! Recently, I became aware of the similar structures between mathematics,
English syntax, and computer languages. Of course, I mean this in a metaphorical
sense. I have also noticed the similarity between computer languages and these
other fields.
In my opinion, these fields share abstract intellectual aspects. It is similar to looking at
the same scene from different angles or perspectives. This realization has enabled me
to make correlations between {M, E, C} in a more sophisticated way. I believe that
adding philosophy as a ‘P’ to this set of intellectual units will make the connections
even more sophisticated.
Therefore, for me, {M, E, C, P} represent a unified set of intellectual units that
I can manipulate with ease due to this awareness. I have noticed that many Japanese people are prone to conform easily to the
majority's opinions or authority figures, such as celebrities who often appear
on TV or social media as representatives of the public. This phenomenon is
known as "seken" in Japan, and many Japanese tend to evaluate their own
value based on these majority opinions or measures.
As a result, Japanese society can be vulnerable to conformity and lack of
independent thinking. To overcome this conventional defect, we need to establish
a self-maximizing or rigid axis that is well thought-out for our authentic purposes
and long-term vision.
I believe that by constantly maintaining our own principles or maxims, we can
illuminate our path whenever we need to clarify our vision and perspectives.
As you know, majority opinions tend to be variable and unreliable, so it is better
not to rely on them. Instead, we should strive to develop our own genuine maxims.
This could also be called an individual philosophy. >>101 ○ establish a self-maxims >>101 ○ establish a self-maxim >>101 ○ be vulnerable to autonomy This is a matrix multiplication problem with a given matrix A of size 4x4 and
matrix B of size 4x2. The matrices are divided into four blocks of size 2x2 and
2x1, respectively, and are denoted by a_1, a_2, a_3, a_4, and b_1, b_2, b_3, b_4.
The resulting matrix C is of size 4x2 and is also divided into four blocks of size 2x1,
denoted by c_1, c_2, c_3, and c_4.
The calculations are shown as follows:
c_1 = (a_1 * b_1) + (a_2 * b_3)
c_2 = (a_1 * b_2) + (a_2 * b_4)
c_3 = (a_3 * b_1) + (a_4 * b_3)
c_4 = (a_3 * b_2) + (a_4 * b_4)
These calculations show that to get the value of each block in C, you need to multiply
the corresponding blocks of A and B and then add the results of these multiplications.
The symbol * denotes matrix multiplication, and + denotes matrix addition. A =
[ 1.0, 0.0, 2.0, 1.0
, 2.0, -1.0, 0.0, 1.0
, 0.0, 1.0, 3.0, 1.0
, 1.0, 1.0, 0.0, 0.0 ]
=
[ a_1, a_2
,a_3, a_4 ]
=
a_1 =
[ 1.0, 0.0
,2.0, -1.0 ]
a_2 =
[ 2.0, 1.0
,0.0, 1.0 ]
a_3 =
[ 0.0, 1.0
,1.0, 1.0 ]
a_4 =
[ 3.0, 1.0
,0.0, 0.0 ] B =
[ -1.0, 1.0
, 0.0, 1.0
, 1.0, -2.0
, 1.0, 2.0 ]
=
[ b_1, b_2
,b_3, b_4 ]
=
b_1 =
[ -1.0
, 0.0 ]
b_2 =
[ 1.0
, 1.0 ]
b_3 =
[ 1.0
, 1.0 ]
b_4 =
[ -2.0
, 2.0 ] C =
[ 2.0, -1.0
, -1.0, 3.0
, 4.0, -3.0
, -1.0, 2.0 ]
=
[ c_1, c_2
,c_3, c_4 ]
=
c_1=
[ 2.0
, -1.0 ]
c_2 =
[ -1.0
, 3.0 ]
c_3 =
[ 4.0
, -1.0 ]
c_4 =
[ -3.0
, 2.0 ] c_1 = (a_1*b_1) + (a_2*b_3)
c_1 = a_1 Numeric.LinearAlgebra.<> b_1 + a_2 Numeric.LinearAlgebra.<> b_3
c_1 =
[ 2.0
, -1.0 ]
c_2 = (a_1*b_2) + (a_2+b_4)
c_2 = a_1 Numeric.LinearAlgebra.<> b_2 + a_2 Numeric.LinearAlgebra.<> b_4
c_2 =
[ -1.0
, 3.0 ] c_3 = (a_3*b_1) + (a_4*b_3)
c_3 = a_3 Numeric.LinearAlgebra.<> b_1 + a_4 Numeric.LinearAlgebra.<> b_3
c_3 =
[ 4.0
, -1.0 ]
c_4 = (a_3*b_2) + (a_4*b_4)
c_4 = a_3 Numeric.LinearAlgebra.<> b_2 + a_4 Numeric.LinearAlgebra.<> b_4
c_4 =
[ -3.0
, 2.0 ] As a result of the products corresponding to each small block a_i and b_i,
values c_1, c_2, c_3, and c_4 are obtained. By rearranging c_1 to c_4, matrix C,
which is the product of matrices A and B, can be obtained as it is.
C =
[ c_1, c_2
, c_3, c_4 ]
=
[ 2.0, -1.0
, -1.0, 3.0
, 4.0, -3.0
, -1.0, 2.0 ]
= Matrix C i.e.
Matrix A * Matrix B = Matrix C
A =
[ 1.0, 0.0, 2.0, 1.0
, 2.0, -1.0, 0.0, 1.0
, 0.0, 1.0, 3.0, 1.0
, 1.0, 1.0, 0.0, 0.0 ]
B =
[ -1.0, 1.0
, 0.0, 1.0
, 1.0, -2.0
, 1.0, 2.0 ]
A * B = C
C =
[ 2.0, -1.0
, -1.0, 3.0
, 4.0, -3.0
, -1.0, 2.0 ] This is equivalent in value to following
A =
[ a_1, a_2
,a_3, a_4 ]
B =
[ b_1, b_2
,b_3, b_4 ]
A * B = C
C =
[ c_1, c_2
,c_3, c_4 ]
=
[ 2.0, -1.0
, -1.0, 3.0
, 4.0, -3.0
, -1.0, 2.0 ]
= Matrix C I am skeptical of materialism and the heavy emphasis on practical learning in Japan.
This approach often leads to tunnel vision and a short-term focus on profits, which
can ultimately diminish social resilience and hinder the development of genuine
intellectual and reasoning abilities.
I believe that this kind of Japanese utilitarianism may have originated from Yukichi Fukuzawa's vision or influence. While his principles may have been appropriate
during his era, they are not as relevant today. In this era of ecological awareness,
we should prioritize reducing unnecessary waste and conforming to ecosystems
to support restoration, rather than producing for the sake of wealth and power.
Therefore, we need a more objective and well-thought-out approach that considers
the long-term future and the well-being of generations to come. Cayley-Hamilton theorem
The theorem states that for a square matrix A, the equation
A² - (a + d)A + (ad - bc)E = O holds true, where:
・ "a + d" is the sum of diagonal elements (denoted as tr A, read as "trace of A")
・ "ad - bc" is the determinant of A (or det A or |A| or Δ("delta"))
・ 'E' is the identity matrix For example, let A be a matrix:
A =
[ a, b
,c, d ]
Suppose we have the matrix:
A =
[ 2.0, 1.0
, -1.0, 4.0 ]
Then we have:
A² =
[ 3.0, 6.0
, -6.0, 15.0 ]
a + d = 6
det A (= ad-bc) = 9
E =
[ 1.0, 0.0
, 0.0, 1.0 ] Thus, we can verify that : A² - (a + d)A + (ad - bc)E = O
[ 3.0, 6.0
, -6.0, 15.0 ]
-
[ 12.0, 6.0
, -6.0, 24.0 ]
+
[ 9.0, 0.0
, 0.0, 9.0 ]
=
[ 0.0, 0.0
, 0.0, 0.0 ]
= Matrix O. A Language Game :
This game is best played with another person whose primary language is
your secondary language. Choose a word or phrase from your primary language
and translate it into your secondary language.
For example, if English is your primary language, you might translate the words
into Spanish. You would then ask the person you are playing with to translate
the Spanish back into English. Continue taking turns back and forth until
each person has completed several words or phrases.
Observe the differences in meaning between the original words of the
primary speaker and those translated back in a secondary language.
Ask the following questions for discussion: 1.How is language important in a living system?
2.What can happen when two systems, that have different languages,
must communicate?
3.What problems can arise when two systems with different languages try
to communicate?
4.What solutions might help address the problems that can arise when
two systems with different languages need to communicate? There is a move to help people communicate across different languages
by using Artificial Intelligence. This can solve some communication problems,
but there is also the potential for some meaning to be lost by having a computer translate.
To avoid this, there is a recognition that translation does require input from a human being.
Translations always have an author and are copyrighted. As we become more connected
in our world, our extensive global communications network has become a system of its own.
It is interconnected and interdependent with language subsystems. We need to be respectful,
tolerant, and appreciative of diversity. We should be open to the possibility of learning
from language and cultures that are quite different from our own and be kind and
ethical global citizens. Researchers found, in a study at the Royal College of Psychiatrist,
that writing about stressful or emotional event has found to
result in both physical and psychological health improvements.
Accordingly, de-clutter your mind with regularity. Let's commence today with happiness. "The most powerful words in the universe are the words you say to yourself" (Marie Forleo) I have observed ongoing debates regarding anti-natalism, and
I believe it is important for those involved to unwind and soothe their static
thoughts and mannerisms. It is also crucial to be aware of the potential
for distorted thinking and avoid being indecisive.
When feeling on edge, it can be difficult to make sound judgments and
consider multifaceted views. It is important to maintain a calm and
open mind when encountering unfamiliar ideas or perspectives.
Anti-natalism is not a hair-raising ideology; rather, it contains facets that
consider the sustainability of our ecosystem. Therefore, one cannot simply
dismiss anti-natalism as having no rhyme or reason. If you have sufficient imagination, you can try to put yourself in the shoes of
someone who is facing severe problems or difficulties in the world. I believe
anti-natalism offers some elements that can alleviate human suffering in the
imaginary realms, and this seems obvious to me.
Rather than getting stuck in debates, we need to find new ways of thinking
and stances. On a daily basis, we encounter or observe many fatal tragedies
in this society, which I call the violence of randomness. I detest such accidents
and unexpected events.
We need to sort out the historical tragedies and predicaments that humans have
faced and try to find ways to prevent them from happening again. This distinction is important because many in and around the AI community assume
that consciousness is just a function of intelligence: that as machines become smarter,
there will come a point at which they also become aware—at which the inner lights
come on for them.
Last March, OpenAI’s chief scientist Ilya Sutskever tweeted, “It may be that today’s
large language models are slightly conscious.” Not long after, Google Research vice
president Blaise Agüera y Arcas suggested that AI was making strides toward consciousness. FLESH AND BLOOD: Being conscious is not the result of some complicated algorithm
running on the wetware of the brain. It is rooted in the fundamental biological drive
within living organisms to keep on living. There are two main reasons why creating artificial consciousness, whether deliberately or
inadvertently, is a very bad idea. The first is that it may endow AI systems with new powers
and capabilities that could wreak havoc if not properly designed and regulated.
Ensuring that AI systems act in ways compatible with well-specified human values is
hard enough as things are. With conscious AI, it gets a lot more challenging, since
these systems will have their own interests rather than just the interests humans give them. The second reason is even more disquieting: The dawn of conscious machines will
introduce vast new potential for suffering in the world, suffering we might not even
be able to recognize, and which might flicker into existence in innumerable server
farms at the click of a mouse.
As the German philosopher Thomas Metzinger has noted, this would precipitate
an unprecedented moral and ethical crisis because once something is conscious,
we have a responsibility toward its welfare, especially if we created it. The problem
wasn’t that Frankenstein’s creature came to life; it was that it was conscious and could feel. Sometimes I imagine a world consisting of two dimensions, a world that is purely
data-driven and free.
In such a world, there would be no need for eating, drinking, washing, or
performing other mundane tasks. No time would be wasted on digestion,
egestion, or other domestic duties, and we could focus on more important matters.
This two-dimensional world would also be suitable for a sustainable ecosystem,
and one could live anywhere, even on the moon, with ease. The world would be
entirely data-driven and liberated, enabling one to change their attributes effortlessly.
I call it a stunning world. Therefore, this new approach suggests a data-driven world for post-humans.
I believe that we no longer need vulnerable actual human beings (AHBs);
instead, they can be replaced with non-actual human beings. Technologically,
this may not be impossible in the coming decades. i.e., only recognition is needed; bodily entity and materiality are not necessary. Penrose tiling are aperiodic tilings obtained using typically 2 isosceles triangles with two
type of edge labelings (so 4 types of triangles). A way to generate the tiling is by applying
iterative edge splitting using the golden ratio. Luckily, our universe seems to run on lawful processes that enable us to learn about
the universe by assuming that the universe is lawful. What’s more, it seems that
the universe runs on simpler – rather than more complex – rules; an intuition
encoded in Occam’s Razor. As the authors state: “There may be a universe where Leonardo da Vinci is not a polymath,
a universe where learning problems have very different structure and therefore preclude
general-purpose solvers, but it is not our universe.” Unlike other particles, entangled non-abelian anyons share a memory of their quantum history. “Compute” is the most basic form of intelligence. Quantum systems may not
propagate like classical systems, but they still “compute” Considering things from a stochastic point of view, it may appear that life is messy,
merely scattered entropies. However, in fact, the state of things would not be so simple.
The universe follows certain explicit prescriptions, this is implicating that reality cannot
be described solely as scattered entropies. Presumably, it may be better described
as the entropy of intermediate or transient jellied states. Today, I learned LaTeX programming in English. The file below is what I just
created using LaTeX format. It looks visually appealing. I feel a sense of satisfaction,
as I was able to work with it in English, which is not my mother tongue.
https://i.imgur.com/7lmjJt0.png I believe that the reason why greedy capitalism has become prevalent is
the existence of too many uninformed individuals. These people are thoughtless
and easily influenced by relentless commercialism through constant exposure
to worthless TV. Today, I've been practicing coding in the LaTeX format, as shown below.
In the figure, you can see some familiar mathematical symbols, such as integral
and sigma signs. I have also become proficient in working with matrices in the
LaTeX format.
https://i.imgur.com/BnrdE9r.png When I took a walk earlier this morning, I saw the moon in the dawn sky.
It appeared as a thin eyebrow or a circular arc. The moon brought a slight
sense of tranquility to my emotions. Sometimes, I feel that the entire natural
world is composed of a mathematical cosmos. Dimensional Analysis Elisabeth Jensen’s dimensional analysis is an analytical
method to clarify and explore the scope and limits of a problem. It examines
five elements of a problem: substantive, spatial, temporal, quantitative, and
qualitative dimensions.
The purpose of these dimensions is to answer the five crucial questions:
what, where, when, how much, and how serious. These questions are further
evaluated by answering specific questions. Dimensional analysis is broken down by using the following five techniques:
Write down the problem; Quickly describe the problem in terms of: What?
Where? When? How much? How serious? Use the descriptions to address
the questions in each dimension (see chart below)
Analyze your responses to the questions by thinking about their implications
and their effect on solving problems. Choose which areas are most applicable
to the problem and need additional analysis.
https://i.imgur.com/2X41ktB.png
(plotted by myself in LaTeX format with table format) I : What is this intrinsic mean or lesson?
the polished floor … often causes mischiefs—bruises, sprains, dislocations — Herbert Spencer ChatGPT :
In the context of the given quote by Herbert Spencer, the term "intrinsic"
refers to a quality or characteristic that is inherent or inherent to something,
in this case, the polished floor.
The phrase "the polished floor … often causes mischiefs—bruises, sprains,
dislocations"suggests that the polished floor itself possesses a certain inherent
quality or characteristic that leads to accidents or injuries such as bruises, sprains,
and dislocations. The emphasis here is on the nature of the polished floor, which
inherently poses a risk or danger to people, rather than external factors or individual
behavior. Herbert Spencer is highlighting the potential dangers of a polished floor, suggesting
that its inherent nature or quality makes it more likely to cause accidents or injuries.
The lesson or meaning conveyed is that even seemingly harmless or well-maintained
surfaces can have inherent risks, and one should be cautious or aware of these risks
to prevent harm. I : Well, this is an alarm as to conformity to convention with thoughtless, isn't this? ChatGPT :
Yes, the quote by Herbert Spencer can be seen as an alarm or warning regarding
conformity to convention without thoughtful consideration. By pointing out
the potential dangers and harms associated with the polished floor, Spencer
highlights the need for critical thinking and questioning of conventional norms.
The mention of "mischiefs—bruises, sprains, dislocations" resulting from the
polished floor suggests that blindly adhering to societal norms or following
conventional practices can lead to negative consequences. It serves as a
reminder that blindly conforming to conventions without critical evaluation
can be detrimental to individuals. Spencer's message encourages individuals to think independently, question
established norms, and consider the potential risks or drawbacks associated
with conformity. It emphasizes the importance of thoughtful analysis and
critical examination rather than simply accepting and conforming to conventions
without questioning their validity or potential negative consequences. From this neat illustration by ChatGPT, I could understand the Spencer's remark has
philosophical well insight. So I write down once again.
the polished floor … often causes mischiefs—bruises, sprains, dislocations — Herbert Spencer Today, I decided to give this diary app a try. The overall appearance is
decent, but I find the font used in the app to be less than aesthetically
pleasing. Additionally, the app only offers a limited selection of four fonts,
which is not sufficient to satisfy my personal preferences.
On the positive side, the auto-correction function is helpful in preventing
spelling mistakes, which I tend to make frequently. In the end, I ended up purchasing
this diary app using a prepayment card of download version for Xbox via amazon. The registration process was not easy, as the website's layout on the Microsoft Platform
was confusing and difficult to navigate. If I hadn't discovered a hidden section of the interface
(located below), I wouldn't have been able to complete the purchase of this diary application. Below the appearance of my diary app.This Anpanman’s face is made of myself
by programming not using painting application.
https://i.imgur.com/vcsKwn7.png
https://i.imgur.com/rSo3RmF.png Just now, I watched an anime called "Hitori Bocchi: Life's Alone" and specifically,
the seventh episode titled "Soft Tear." In this episode, four close classmates decided
to spend their summer vacation together by going to the pool and karaoke.
My favorite character in this anime is Naco. On the surface, Naco appears
cool and gruff, but in reality, she is kind and thoughtful. Since Naco doesn't
know how to swim, Bocchi, who is a close friend of Naco's classmates,
taught herhow to swim. I really enjoy watching "Hitori Bocchi: Life's Alone." The reason for this is
the excellent portrayal of the friendship among the four girls. It helps me
relax and unwind from any stress or tension I may be feeling.
Therefore, I plan to continue watching this anime at my own pace to
stay connected with the story.
https://i.imgur.com/XMnX6L4.png >>156
○ taught her how to swim. Just now, I purchased a concept note application for my PC. It has a visually appealing
interface, and I am looking forward to using it. As a trial, I created a visual representation
of Euler's famous identity formula and a 2x2 identity matrix.
In square matrices, it is known that the determinant of a matrix and the determinant of
its transpose are equivalent.
https://i.imgur.com/fh4QJOD.png Heron's formula is used to calculate the area of a triangle based on
its three side lengths.
https://i.imgur.com/aAp13uk.png https://illusionsetc.blogspot.com/2005/12/checker-shadow-optical-illusion.html
Checker Shadow Optical Illusion Revisited
It occurred to me today that the Checker Shadow Optical Illusion that I presented here could have been better presented if it fit my blogs color scheme so I decided to modify the original. I gave it a black background and changed the light source.
The bottom line is still the same. Square A and Square B below are the exact same color. Hard to believe isn't it?
I look at this and find it hard to believe. But I used the extension in Firefox called colorzilla which provides you with an eyedropper tool. I checked both of squares and sure enough the RGB values of the grays in both square A and square B are 135-135-135. Shapley values underlie one of the most popular model-agnostic
methods within explainable artificial intelligence. These values are
designed to attribute the difference between a model’s prediction
and an average baseline to the different features used as input to
the model.
Being based on solid game-theoretic principles,Shapley values uniquely
satisfy several desirable properties, which is why they are increasingly
used to explain the predictions of possibly complex and highly
non-linear machine learning models. Shapley values are well calibrated
to a user’s intuition when features are independent, but may lead to
undesirable,counterintuitive explanations when the independence
assumption is violated. In this paper, we propose a novel framework for computing Shapley
values thatgeneralizes recent work that aims to circumvent the
independence assumption.By employing Pearl’s do-calculus, we show
how these ‘causal’ Shapley values can be derived for general causal
graphs without sacrificing any of their desirable properties.
Moreover, causal Shapley values enable us to separate the contribution
of direct and indirect effects. We provide a practical implementation
for computing causal Shapley values based on causal chain graphs when
only partial information is available and illustrate their utility on
a real-world example. A broad coalition of AI experts recently released a brief public statement
warning of “the risk of extinction from AI.” There are many different ways
in which AIs might become serious dangers to humanity, and the exact
nature of the risks is still debated, but imagine a CEO who acquires
an AI assistant.
They begin by giving it simple, low-level assignments, like drafting emails
and suggesting purchases. As the AI improves over time, it progressively
becomes much better at these things than their employees. So the AI
gets “promoted.” Rather than drafting emails, it now has full control of
the inbox. Rather than suggesting purchases, it’s eventually allowed
to access bank accounts and buy things automatically. At first, the CEO carefully monitors the work, but as months go
by without error, the AI receives less oversight and more autonomy
in the name of efficiency. It occurs to the CEO that since the AI
is so good at these tasks, it should take on a wider range of more
open-ended goals: “Design the next model in a product line,”
“plan a new marketing campaign,” or “exploit security flaws in a
competitor’s computer systems.”
The CEO observes how businesses with more restricted use of
AIs are falling behind, and is further incentivized to hand over
more power to the AI with less oversight. Companies that resist
these trends don’t stand a chance. Eventually, even the CEO’s
role is largely nominal. The economy is run by autonomous These same competitive dynamics will apply not just to companies
but also to nations. As the autonomy of AIs increases, so will their
control over the key decisions that influence society. If this happens,
our future will be highly dependent on the nature of these AI agents.
The good news is that we have a say in shaping what they will be like.
The bad news is that Darwin’s laws do too. Though we think of natural
selection as a biological phenomenon, its principles guide much more,
from economies to technologies. The evolutionary biologist
Richard Lewontin proposed that natural selection will take hold in any
environment where three conditions are present:
1) there are differences between individuals, 2) characteristics are
passed on to future generations, and 3) the fittest variants propagate
more successfully. Consider the content-recommendation algorithms used by social
media platforms and streaming services. When particularly addictive
algorithms hook users, they result in higher engagement and screen time.
These more effective algorithms are consequently “selected” and
further fine-tuned, while algorithms that fail to capture attention are
discontinued. This fosters the survival of the most addictive dynamic.
Platforms that refuse to use addictive methods are simply outcompeted
by platforms that do, leading to a race to the bottom among competitors
that has already caused massive harm to society. In the biological realm, evolution is a slow process. For humans, it takes
nine months to create the next generation and around 20 years of
schooling and parenting to produce fully functional adults. But scientists
have observed meaningful evolutionary changes in species with rapid
reproduction rates, like fruit flies, in fewer than 10 generations.
Unconstrained by biology, AIs could adapt—and therefore evolve—
even faster than fruit flies do.
There are three reasons this should worry us. The first is that selection
effects make AIs difficult to control. Whereas AI researchers once spoke of “designing” AIs, they now speak of “steering” them. And even our ability
to steer is slipping out of our grasp as we let AIs teach themselves and increasingly act in ways that even their creators do not fully understand. In advanced artificial neural networks, we understand the inputs that
go into the system, but the output emerges from a “black box” with a
decision-making process largely indecipherable to humans.
Second, evolution tends to produce selfish behavior. Amoral competition
among AIs may select for undesirable traits. AIs that successfully gain
influence and provide economic value will predominate, replacing AIs
that act in a more narrow and constrained manner, even if this comes
at the cost of lowering guardrails and safety measures. As an example, most businesses follow laws, but in situations where
stealing trade secrets or deceiving regulators is highly lucrative and
difficult to detect, a business that engages in such selfish behavior
will most likely outperform its more principled competitors.
Selfishness doesn’t require malice or even sentience. When an AI
automates a task and leaves a human jobless, this is selfish behavior
without any intent. If competitive pressures continue to drive AI
development, we shouldn’t be surprised if they act selfishly too. The third reason is that evolutionary pressure will likely ingrain AIs
with behaviors that promote self-preservation. Skeptics of AI risks
often ask, “Couldn’t we just turn the AI off?” There are a variety of
practical challenges here. The AI could be under the control of a
different nation or a bad actor.
Or AIs could be integrated into vital infrastructure, like power grids or
the internet. When embedded into these critical systems, the cost of
disabling them may prove too high for us to accept since we would
become dependent on them. AIs could become embedded in our
world in ways that we can’t easily reverse. But natural selection poses a
more fundamental barrier: we will select against AIs that are easy to
turn off, and we will come to depend on AIs that we are less likely to turn off. These strong economic and strategic pressures to adopt the systems
that are most effective mean that humans are incentivized to cede more
and more power to AI systems that cannot be reliably controlled, putting
us on a pathway toward being supplanted as the earth’s dominant species.
There are no easy, surefire solutions to our predicament.
A possible starting point would be to address the remarkable lack of
regulation of the AI industry, which currently operates with little oversight,
much of the research taking place in the dark. Regulation needs to be done proactively rather than reactively; if something goes wrong in this domain,
we may not get the chance to fix it. The problem, however, is that competition within and between
nations pushes against any common-sense safety measures. AI is
big -business. In 2015, total corporate investment in AI was $12.7 billion.
By 2021, this figure had grown to $93.5 billion. As the race toward
powerful AI systems quickens, corporations and governments are
increasingly incentivized to reach the finish line first. We need research
on AI safety to progress as quickly as research on improving AI capabilities.
There aren’t many market incentives for this, so governments should
offer robust funding as soon as possible.
The future of humanity is closely intertwined with the progression of AI.
It is therefore a disturbing realization that natural selection may have
more sway over it than we do. But as of now, we are still in command.
It is time to take this threat seriously. Once we hand over control,
we won’t get it back. It was automation, I know.
That was what was making the factory go.
It was IBM, it was Univac,
It was all those gears going clickety clack, dear.
I thought automation was keen
Till you were replaced by a ten-ton machine.
It was a computer that tore us apart, dear,
Automation broke my heart. . . . It was automation,
I’m told,That’s why I got fired and I’m out
in the cold.How could I have known, when the 503
Started in to blink, it was winking at me, dear?
I thought it was just some mishap
When it sidled over and sat on my lap.
But when it said “I love you” and gave me a hug, dear,
That’s when I pulled out . . . its . . . plug. ■ このスレッドは過去ログ倉庫に格納されています
