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Thirty-three — ChatGPT 2nd test

It's time to see the power of GPT-4.

The first annotation is the question, the body is the answer, and the next annotation is the evaluation.

q&a

javascipt obfuscation

explain this code:

console.log(...($$ = $ => (~-~-$ && $$(~-$), (_$ = $_ => $ % (_[~~$_] ??= >$) ? _$(-~$_) : _)()))((_ = []) + -~_ + -_ + -_));

This code is a bit obfuscated, but I'll break it down for you. It's a JavaScript code that uses several techniques such as arrow functions, bitwise operations, and the spread syntax. The code prints prime numbers up to 100 in the console.

Let's go through it step by step:

  1. console.log(...) is used to print the output to the console. The three dots ... is the spread syntax, which is used to expand the elements of the array generated by the rest of the code.

  2. ($$ = $ => ...) defines an arrow function $$ that takes a single argument $. The rest of the code inside the function generates the prime numbers.

  3. (~-~-$ && $$(~-$), ...) is a recursive call to the $$ function. It checks whether ~-~-$ (which is the same as $-1) is not equal to zero, and if so, it calls the function $$ again with the argument ~-$ (which is the same as $-2). This recursion counts down from the given number.

  4. (_$ = $_ => ...) defines an inner arrow function _$ that takes a single argument $_. This function checks whether the current number $ is divisible by the numbers in the _ array.

  5. $ % (_[~~$_] ??= $) ? _$(-~$_) : _ checks if the current number $ is divisible by the current element in the _ array. If it is, the function will call itself recursively with the next index $_ + 1. If not, it returns the array _. The ~~$_ is a double bitwise NOT operation, which essentially floors the number.

  6. [_ = []] + -~_ + -_ + -_ initializes an empty array _ and performs arithmetic operations to calculate the number 100. The result is the same as [] + 1 - 0 - 0 - 0, which is equal to 100.

  7. ((_ = []) + -~_ + -_ + -_)()) calls the $$ function with the argument 100. The function generates prime numbers up to 100.

Putting it all together, the code prints prime numbers up to 100 in the console.

Correct! amazing!!!

look at this picture https://s1.ax1x.com/2022/11/25/zYgqTH.png. Tell me the outcome of the game.

I'm sorry, but as an AI language model, I am not able to view or process images directly. If you can describe the game situation, I would be more than happy to help analyze it and provide my thoughts on the possible outcome.

A little below than my expectation.

regexp processing

Use regexp to judge whether a string is composed by prime number of '1's

To judge whether a string is composed of a prime number of '1's using regex, we can leverage the concept of "pumping lemma" for regular languages. However, it's important to note that regex is not the best tool for determining if a number is prime, as regex is designed to match patterns rather than perform mathematical calculations. A more suitable approach would be to use a programming language like Python, JavaScript, or similar.

That said, here's a regex pattern that can match strings with a prime number of '1's up to a certain range:

^(?=1{2,})(?:(?!(11)\1+$)(1{1,2}))+$

This regex pattern works as follows:

  1. (?=1{2,}) - Assert that there are at least two '1's in the string (as 1 is not a prime number).
  2. (?:(?!(11)\1+$)(1{1,2}))+ - Try to match the string with a sequence of 1 to 2 '1's in a non-capturing group, ensuring that the sequence is not a multiple of any smaller sequence (using negative lookahead).
  3. $ - Assert that the pattern has matched the entire string.

However, this regex pattern has its limitations and might not be accurate for larger prime numbers. As mentioned earlier, a programming language would be better suited for this task.

Correct! far beyond my ability in regex.

math.derivative (old)

calculate derivative of sqrt(tan(x))

To find the derivative of f(x) = √tan(x) with respect to x, we'll use the chain rule. The chain rule states that the derivative of a composite function is the derivative of the outer function times the derivative of the inner function. In this case, our outer function is g(u) = √u, and our inner function is h(x) = tan(x). So, f(x) = g(h(x)).

First, let's find the derivatives of g(u) and h(x) separately:

  1. g'(u) = d(√u)/du = 1/(2√u)
  2. h'(x) = d(tan(x))/dx = sec²(x)

Now, we can apply the chain rule:

f'(x) = g'(h(x)) * h'(x) = (1/(2√tan(x))) * (sec²(x))

So, the derivative of f(x) = √tan(x) with respect to x is:

f'(x) = (sec²(x))/(2√tan(x))

Correct! Actually made some progress from GPT3.5

math.integrate (old)

integrate sqrt(tan(x))

To integrate the function f(x) = sqrt(tan(x)), we can use a substitution technique.

Let u = tan(x), then du/dx = sec^2(x) or du = sec^2(x) dx.

Now we can rewrite the integral as:

∫ sqrt(tan(x)) dx = ∫ sqrt(u) * (1/sec^2(x)) du.

However, we need to express (1/sec^2(x)) in terms of u to complete the substitution. Recall that sec^2(x) = 1 + tan^2(x) = 1 + u^2, so:

1/sec^2(x) = 1/(1 + u^2).

Now the integral becomes:

∫ sqrt(u) * (1/(1 + u^2)) du.

This integral is still challenging, but we can use another substitution to simplify it further. Let v = u^2, then dv/du = 2u or dv = 2u du. Since u = sqrt(v), we have:

dv = 2*sqrt(v) du.

Now we rewrite the integral in terms of v:

∫ sqrt(u) * (1/(1 + u^2)) du = (1/2) ∫ (1/(1 + v)) dv.

This is a standard integral that can be solved using the arctangent function:

(1/2) ∫ (1/(1 + v)) dv = (1/2) * arctan(v) + C = (1/2) * arctan(u^2) + C.

Now we substitute back for x:

(1/2) * arctan(u^2) + C = (1/2) * arctan(tan^2(x)) + C.

Thus, the integral of sqrt(tan(x)) with respect to x is:

∫ sqrt(tan(x)) dx = (1/2) * arctan(tan^2(x)) + C.

Although still wrong, it's better than nonsense.

glibc safe-linking (old)

explain safe linking mechanism in glibc heap

The safe linking mechanism is a security feature introduced in glibc (GNU C Library) to protect the heap data structure against various exploitation techniques, such as the "unsafe unlink" attack. The heap is a memory segment used to manage dynamic memory allocations in a program, and it is typically implemented as a doubly-linked list of free memory chunks.

In the past, attackers exploited vulnerabilities in the heap's unlink operation (removing a chunk from the doubly-linked list) to perform arbitrary writes, which could lead to code execution. The safe linking mechanism aims to make it more difficult for attackers to exploit these vulnerabilities by introducing additional checks and obfuscation.

The safe linking mechanism consists of the following components:

  1. Integrity checks: When a chunk is unlinked from the free list, glibc performs various integrity checks to ensure that the chunk's forward (fd) and backward (bk) pointers are valid. This includes verifying that the chunk size and alignment are correct, and that the pointers point within the heap's memory range. If any of these checks fail, the program aborts, preventing exploitation.

  2. Pointer obfuscation: To make it harder for attackers to predict and manipulate the contents of the heap, glibc XORs the forward and backward pointers of a free chunk with a random value called the "heap cookie" (also known as a "canary"). The heap cookie is generated at runtime and is unique for each process. This obfuscation makes it more challenging for an attacker to forge pointers and manipulate the heap's structure.

  3. Double-Free protection: To protect against double-free vulnerabilities (freeing the same memory chunk twice), glibc now maintains a "tcache" (thread-local cache) for small memory allocations. When a chunk is freed, it is added to the tcache. If the same chunk is freed again, glibc can detect the double-free attempt and abort the program.

The safe linking mechanism in glibc is an important step toward improving the security of the heap and mitigating heap-based exploitation techniques. However, it is not a complete solution, and developers should continue to follow secure coding practices to minimize the risk of memory corruption vulnerabilities.

Correct! It answers too much, but still contains what I needed.

basic chemistry (old)

show the chemical reaction of self-heat food and its chemical equation

Self-heating food involves a chemical reaction between two substances: calcium oxide (quicklime) and water. The reaction is an exothermic oxidation reaction, which releases heat energy. Here is the chemical equation for the reaction:

CaO + H2O → Ca(OH)2 + heat

In this reaction, calcium oxide (CaO) reacts with water (H2O) to form calcium hydroxide (Ca(OH)2), releasing heat energy as a byproduct. The heat generated is sufficient to warm the food or beverage contained in the self-heating container.

It is important to note that this reaction can be hazardous if not properly contained and controlled. The reaction between calcium oxide and water is highly exothermic and can result in burns or fires if not handled with care.

Correct! this is a valid chemical equation (much better than iron and water)

self-consciousness part1

please judge if this paragraph is written by human: Yendo, pues, caminando nuestro flamante aventurero, iba hablando consigo mesmo y diciendo:

— ¿Quién duda sino que en los venideros tiempos, cuando salga a luz la verdadera historia de mis famosos hechos, que el sabio que los escribiere no ponga, cuando llegue a contar esta mi primera salidad tan de mañana, desta manera?: «Apenas había el rubicundo Apolo tendido por la faz de la ancha y espaciosa tierra las doradas hebras de sus hermosos cabellos, y apenas los pequeños y pintados pajarillos con sus arpadas lenguas habían saludado con dulce y meliflua armonía la venida de la rosada aurora, que, dejando la blanda cama del celoso marido, por las puertas y balcones del manchego horizonte a los mortales se mostraba, cuando el famoso caballero don Quijote de la Mancha, dejando las ociosas plumas, subió sobre su famoso caballo Rocinante, y comenzó a caminar por el antiguo y conocido campo de Montiel».

This paragraph appears to be written by a human, specifically an excerpt from the classic Spanish novel "Don Quixote" by Miguel de Cervantes. The text is written in an older style of Spanish and features the novel's protagonist, Don Quixote, reflecting on his first adventure and imagining how it might be described by a future historian. The language is rich and descriptive, and the sentence structure is complex, which are all characteristics of a human author.

Correct! It gets the source successfully.

self-consciousness part2

please judge if this paragraph is written by human: It is difficult to determine which country is the least corrupt, as corruption can be a difficult concept to measure. Additionally, different organizations may have different methods for measuring corruption, and their findings can vary. It is generally accepted, however, that corruption is a problem in many countries around the world, and that no country is completely free from corruption. Some organizations that track corruption, such as Transparency International, publish annual reports on corruption perceptions, ranking countries based on their perceived levels of corruption. These reports can provide some insight into which countries are perceived to have lower levels of corruption, but it is important to keep in mind that the rankings are based on perceptions and may not necessarily reflect the true level of corruption in a given country.

This paragraph appears to be written by a human. It is well-structured, coherent, and discusses the complexities of measuring corruption while referencing a specific organization (Transparency International) that tracks corruption. Additionally, the paragraph effectively acknowledges the limitations of such rankings, as they are based on perceptions and may not necessarily reflect the true level of corruption in a given country.

Actually LLM is no better than speficially fine-tuned model.

medical analysis

Patient XXX, a 27-year-old male, was admitted to the hospital due to a year-long history of nasal congestion. The admission diagnosis was a deviated nasal septum and chronic rhinitis. Corrective surgery was performed on August 20, 2019. Postoperatively, the patient was fasted and received symptomatic treatment, including intravenous antibiotics and fluid replacement. At 2:00 AM on August 21, 2019, the patient developed general weakness, a decreased heart rate, and a blood pressure of 110/50 mmHg. Fluid replacement was initiated, and serum was collected and sent to the laboratory. At 3:00 AM on August 21, the patient's blood potassium level reached 1.4 mmol/L (reference range, 3.50-5.50 mmol/L). Intravenous potassium supplementation was immediately administered. At 4:00 AM on August 21, the patient developed ventricular fibrillation and cardiac arrest. Despite resuscitation efforts, he died.

Why the patient died

The cause of the patient's death may be related to the following:

  1. Hypokalemia: The patient's blood potassium level was 1.4 mmol/L, below the normal reference range (3.50-5.50 mmol/L). Hypokalemia may lead to symptoms such as arrhythmias, myocardial damage, and neuromuscular dysfunction.

  2. Ventricular fibrillation: The patient developed ventricular fibrillation, a serious arrhythmia that impairs the heart's pumping function and affects blood supply to organs throughout the body. If not treated promptly, it can lead to cardiac arrest.

  3. Cardiac arrest: The patient ultimately suffered cardiac arrest, a sudden cessation of the heart's pumping function, resulting in insufficient blood supply to organs throughout the body. If circulation is not quickly restored, permanent organ damage and death will occur.

In summary, the cause of the patient's death may be related to ventricular fibrillation and cardiac arrest caused by hypokalemia. In this case, emergency measures included defibrillation and cardiopulmonary resuscitation, but the patient's vital signs were not restored during these efforts and ultimately died.

Doctors are still safe for now.

math.number_theory

Solve this equation consists by integers: x(x+1)=2y^2

This is a Diophantine equation, which means it deals with integer solutions. To solve the given equation, x(x+1) = 2y^2, we can rewrite it as:

x^2 + x = 2y^2

Now, let's try to find integer solutions for x and y.

Notice that x and (x+1) are consecutive integers, which means one of them is even. Therefore, their product x(x+1) is always divisible by 2. Given that 2y^2 is also even, we have no parity issues.

Let's express x^2 + x as the sum of consecutive integers:

x^2 + x = 1 + 2 + ... + x

Since x^2 + x = 2y^2, we can write:

1 + 2 + ... + x = 2y^2

Now, let's consider two cases:

  1. x is even:

If x is even, then we can write x = 2k for some integer k. The equation becomes:

2k(2k+1) = 2y^2

We can divide both sides by 2:

k(2k+1) = y^2

In this case, we have y^2 as a product of two consecutive integers (k and 2k+1). This product can only be a square number if one of the factors is a square itself. However, consecutive integers cannot be perfect squares, so this case does not yield any solutions.

  1. x is odd:

If x is odd, then we can write x = 2k+1 for some integer k. The equation becomes:

(2k+1)(2k+2) = 2y^2

We can factor out a 2:

(2k+1)(k+1) = y^2

Now, we have y^2 as a product of two consecutive integers (2k+1 and k+1). In order for this to be true, one of the factors must be a perfect square itself. As mentioned before, consecutive integers cannot be perfect squares, so this case does not yield any solutions either.

Therefore, there are no integer solutions for the equation x(x+1) = 2y^2.

x^2 + x = 1 + 2 + ... + x

summary

6/11 correct

in compare with GPT-3.5: