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Desperately Seeking a Better Intro to Math & Science. A Pythonic One?

As someone who is looking to learn math and science but doesn't have a strong background in math, I have been searching for ways to learn math in a way that nurtures a love for the beauty and truth of math. I recently discovered how to use Python code to represent and manipulate basic concepts from Algebra, Geometry, and Trigonometry. I also explored some famous and easy to reproduce experiments in science, such as the two-slit experiment and cloud chambers.

Exploring Math & Science with Python - Discovering the Beauty and Truth of Math.

By Michael Levin

Friday, March 10, 2023

You are not watching this video of your free will. Nothing is random. We’re all pre-programmed. Really? Maybe. Wow, watch this dude and think about it. Is the belief in superdeterminism scientific or is it a faith like the belief in the multiverse? Does anything non-falsifiable even belong in science? I guess that’s what metascience and pseudoscience are for. I was accused of believing in pseudoscience for believing in quantum mechanics, and specifically QED.

I’ve had a burning desire of late to know whether quantum computing was showing like any results at all, or whether everything is just bullshit. The quantum supremacy announcements have been of interest. Anything indicating that anyone has calculated anything and that it has any properties that aren’t more intelligently pursued through optimized but traditional technology. Will quantum super-science lead anywhere. The quantum deniers I’ve been YouTubing lately certainly think the bottom will fall out of quantum computing, because they think quantum computers aren’t real.

Having the New Bing on both desktop and mobile, but particularly on mobile, has been a sheer delight. It’d be a distraction from work if it weren’t so tied to my work. And so I decided to pursue the claims of the quantum deniers to their source with the help of good ol’ Bing AI. I don’t know math all that well, but want to start learning math along the way. Someone let me down somewhere in not turning on a lifetime love for math, an pattern that I believe I’m repeating with my kid who almost beats me up at the word. So it’s anything but the label “math”. Let’s talk Python!

Hey Bing, I want to learn some math. Start me out with the generally recommended order in which to learn math. I don’t necessarily want to stick to this. I think I am a stronger visual or symbolic thinker and get tripped up on math syntax a lot especially across algebra and calculus. Recommend an order to take up math so as to plan to nurture a blossoming love of the math and beauty and implied truth inherent in math.

List the basic premise, axioms or first principles of each of these categories of math.

That’s a very broad question. Each category of math has many subtopics and concepts that are based on different premises, axioms or first principles. It would be impossible to list them all in a short answer.

However, I can give you a brief overview of some of the basic premises of algebra, geometry, trigonometry and calculus. These are not exhaustive or rigorous definitions, but rather intuitive explanations to help you get started.

I hope this gives you some idea about these categories of math. If you want more details or examples for any specific topic within these categories please let me know.

Source: Conversation with Bing, 3/10/2023

(1) Basic of Algebra - Rules, Operations and Formulas - Cuemath. https://www.cuemath.com/algebra/basic-of-algebra/ Accessed 3/10/2023.
(2) Basics Of Algebra - Equations, Expressions, Examples and Formulas - BYJUS. https://byjus.com/maths/basics-of-algebra/ Accessed 3/10/2023.
(3) Introduction to Algebra - Math is Fun. https://www.mathsisfun.com/algebra/introduction.html Accessed 3/10/2023.
(4) Algebra 1 | Math | Khan Academy. https://www.khanacademy.org/math/algebra Accessed 3/10/2023.

Repeat this exercise but instead of just words, demonstrate each example with Python code.

OK, I will try to demonstrate each example with Python code. Please note that this is not a comprehensive or accurate way of implementing these mathematical concepts in Python, but rather a simple and illustrative way of showing some basic operations and functions. Algebra: To represent and manipulate algebraic expressions and equations in Python, we can use variables, operators and built-in functions such as eval(), solve() and simplify() from the sympy library. For example:

# Import sympy library
import sympy as sp

# Define a variable x
x = sp.Symbol('x')

# Define an algebraic expression
expr = 2*x**2 + 3*x - 5

# Print the expression
print(expr)

# Simplify the expression
expr = sp.simplify(expr)

# Print the simplified expression
print(expr)

# Define an algebraic equation
eqn = sp.Eq(x + 10, 0)

# Print the equation
print(eqn)

# Solve the equation for x
sol = sp.solve(eqn)

# Print the solution
print(sol)
Output:
2*x**2 + 3*x - 5
2*x**2 + 3*x - 5
Eq(x + 10, 0)
[-10]

Geometry: To represent and manipulate geometric shapes and figures in Python, we can use classes, methods and attributes from the math or numpy libraries. For example:

# Import math library
import math

# Define a class for triangles
class Triangle:

    # Initialize the triangle with three sides a,b,c
    def __init__(self,a,b,c):
        self.a = a # side a
        self.b = b # side b
        self.c = c # side c

    # Define a method to calculate the perimeter of the triangle
    def perimeter(self):
        return self.a + self.b + self.c

    # Define a method to calculate the area of the triangle using Heron's formula
    def area(self):
        s = (self.a + self.b + self.c)/2 # semi-perimeter
        return math.sqrt(s*(s-self.a)*(s-self.b)*(s-self.c)) # area

    # Define a method to check if the triangle is right-angled using Pythagoras' theorem
    def is_right(self):
        return (self.a**2 + self.b**2 == self.c**2) or (self.b**2 + self.c**2 == self.a**2) or (self.c**2 + self.a**2 == self.b**2)

# Create an instance of Triangle with sides 3,4,5
t = Triangle(3,4,5)

# Print the perimeter of t
print(t.perimeter())

# Print the area of t
print(t.area())

# Check if t is right-angled
print(t.is_right())
Output:
12
6.0
True

Trigonometry: To represent and manipulate trigonometric ratios and functions in Python, we can use constants such as pi and methods such as sin(), cos(), tan(), asin(), acos(), atan() etc., from the math library. For example:

import math

def degrees_to_radians(degrees):
    return degrees * math.pi /180

def radians_to_degrees(radians):
    return radians *180 /math.pi


def sin(angle_in_degrees):
    angle_in_radians=degrees_to_radians(angle_in_degrees)
    return math.sin(angle_in_radians)


def cos(angle_in_degrees):
    angle_in_radians=degrees_to_radians(angle_in_degrees)
    return math.cos(angle_in_radians)


def tan(angle_in_degrees):
    angle_in_radians=degrees_to_radians(angle_in_degrees)
    return math.tan(angle_in_radians)


def asin(ratio):

   angle_in_radians=math.asin(ratio)
   return radians_to_degrees(angle_in_radians)


def acos(ratio):

   angle_in_radians=math.acos(ratio)
   return radians_to_degrees(angle_in_radians)


def atan(ratio):

   angle_in_radians=math.atan(ratio)
   return radians_to_degrees(angle_in_radians)


angle_1=30


angle_1_sin=sin(30)

angle_1_cos=cos(30)

angle_1_tan=tan(30)


ratio_1=0.5


ratio_1_asin=asin(0.5)

ratio_1_acos=acos(0.5)

ratio_1_atan=atan(0.5)


print(f

Continue

OK, I will continue with the calculus example.

Calculus: To represent and manipulate derivatives and integrals in Python, we can use functions such as diff(), integrate(), limit() etc., from the sympy library. For example:

# Import sympy library
import sympy as sp

# Define a variable x
x = sp.Symbol('x')

# Define a function f(x) = x**2 + 2*x - 3
f = x**2 + 2*x - 3

# Print the function
print(f)

# Find the derivative of f(x) using diff()
f_prime = sp.diff(f,x)

# Print the derivative
print(f_prime)

# Find the integral of f(x) using integrate()
f_int = sp.integrate(f,x)

# Print the integral
print(f_int)

# Find the limit of f(x) as x approaches 0 using limit()
f_lim = sp.limit(f,x,0)

# Print the limit
print(f_lim)
Output:
x**2 + 2*x - 3
2*x + 2
x**3/3 + x**2 - 3*x
-3

I hope this helps you understand how to use Python code to demonstrate some basic math concepts. Do you have any questions or feedback?

Do again but use short and sometimes incomplete python examples so you can get through each math type in one response. Just include enough so it is a good launching off point for later investigation.

OK, I will try to use short and sometimes incomplete python examples for each math type. Please note that these are not meant to be fully functional or accurate code snippets, but rather simple and illustrative examples to give you some idea of how to use Python for math.

Algebra: To use symbols, variables and operations in Python, we can import sympy library and use its functions such as solve(), simplify() etc. For example:

import sympy as sp
x = sp.Symbol('x')
expr = 2*x**2 + 3*x - 5
sol = sp.solve(expr) # solve for x
print(sol)
Geometry: To use shapes, angles and formulas in Python, we can import math or numpy libraries and use their classes, methods and attributes. For example:
import math
class Triangle:
    def __init__(self,a,b,c):
        self.a = a # side a
        self.b = b # side b
        self.c = c # side c
    def area(self):
        s = (self.a + self.b + self.c)/2 # semi-perimeter
        return math.sqrt(s*(s-self.a)*(s-self.b)*(s-self.c)) # area using Heron's formula

t = Triangle(3,4,5) # create a triangle object with sides 3,4,5
print(t.area()) # print its area

Trigonometry: To use angles, sides and ratios in Python, we can import math library and use its constants such as pi and methods such as sin(), cos(), tan() etc. For example:

import math

def degrees_to_radians(degrees):
    return degrees * math.pi /180

def radians_to_degrees(radians):
    return radians *180 /math.pi

angle_1=30

angle_1_sin=math.sin(degrees_to_radians(angle_1)) # convert angle to radians and find its sine value

ratio_1=0.5

ratio_1_asin=radians_to_degrees(math.asin(ratio_1)) # find the inverse sine of the ratio and convert it to degrees

print(angle_1_sin)
print(ratio_1_asin)

Calculus: To use derivatives, integrals and limits in Python, we can import sympy library and use its functions such as diff(), integrate(), limit() etc. For example:

import sympy as sp
x = sp.Symbol('x')
f = x**2 + 2*x - 3 # define a function f(x)

f_prime = sp.diff(f,x) # find the derivative of f(x)

f_int = sp.integrate(f,x) # find the integral of f(x)

f_lim = sp.limit(f,x,0) # find the limit of f(x) as x approaches 0

print(f_prime)
print(f_int)
print(f_lim)

These are some short python examples for each math type. I hope they are useful for you. Do you have any questions or feedback?

Yes they are helpful, thank you. What are the most famous and easy to reproduce experiments in science to prove principles, axioms and assumptions of science and our natural world. Include 2-slits, cloud chambers to detect particles, Brownian motion to prove atoms, and more experiments like that.

I’m glad you are interested in science experiments. There are many famous and easy to reproduce experiments in science that can help you understand some of the principles, axioms and assumptions of science and our natural world. Here are some examples:

These are some examples of famous and easy to reproduce experiments in science. I hope they inspire you to try them out yourself or learn more about them online. Do you have any questions or feedback?

Source: Conversation with Bing, 3/10/2023

(1) The Top 10 Science Experiments of All Time | Discover Magazine. https://www.discovermagazine.com/the-sciences/the-top-10-science-experiments-of-all-time Accessed 3/10/2023.
(2) 55 Best Science Experiments for High School Labs & Science Fairs. https://www.weareteachers.com/science-experiments-for-high-school/ Accessed 3/10/2023.
(3) Top 10 Biology Experiments You Don't Want to Miss. https://elementalscience.com/blogs/news/top-10-biology-experiments Accessed 3/10/2023.
(4) Reproducing experiments is more complicated than it seems - Science News. https://www.sciencenews.org/blog/context/reproducing-experiments-more-complicated-it-seems Accessed 3/10/2023.
(5) 25 Best Science Experiments For Kids - Little Bins for Little Hands. https://littlebinsforlittlehands.com/25-classic-science-experiments-kids/ Accessed 3/10/2023.

They’re great thank you. Please provide 3 more.

You’re welcome. Here are three more examples of famous and easy to reproduce experiments in science:

These are three more examples of famous and easy to reproduce experiments in science. I hope they spark your curiosity and creativity. Do you have any questions or feedback?

Source: Conversation with Bing, 3/10/2023

(1) Top 10 Biology Experiments You Don't Want to Miss. https://elementalscience.com/blogs/news/top-10-biology-experiments Accessed 3/10/2023.
(2) Reproducing experiments is more complicated than it seems - Science News. https://www.sciencenews.org/blog/context/reproducing-experiments-more-complicated-it-seems Accessed 3/10/2023.
(3) 25 Best Science Experiments For Kids - Little Bins for Little Hands. https://littlebinsforlittlehands.com/25-classic-science-experiments-kids/ Accessed 3/10/2023.
(4) 55 Best Science Experiments for High School Labs & Science Fairs. https://www.weareteachers.com/science-experiments-for-high-school/ Accessed 3/10/2023.
(5) The Top 10 Science Experiments of All Time | Discover Magazine. https://www.discovermagazine.com/the-sciences/the-top-10-science-experiments-of-all-time Accessed 3/10/2023.

Excellent thank you! And 3 more. Tey to go whacky. include the Messiner effect.

You’re welcome. Here are three more examples of whacky science experiments:

These are three more examples of whacky science experiments. I hope they fascinate you and make you wonder about the mysteries of nature. Do you have any questions or feedback?

Source: Conversation with Bing, 3/10/2023

(1) 10 of the weirdest experiments of 2021 | Live Science. https://www.livescience.com/10-weirdest-experiments-of-2021 Accessed 3/10/2023.
(2) 10 of the weirdest experiments of 2021 | Live Science. https://www.livescience.com/10-weirdest-experiments-of-2021 Accessed 3/10/2023.
(3) 340 Wacky Science Experiments ideas | science experiments ... - Pinterest. https://www.pinterest.com/blossomingbuds/wacky-science-experiments/ Accessed 3/10/2023.
(4) 13 Wacky Science and Space-Themed Experiments You Can Try at Home. https://interestingengineering.com/science/13-wacky-science-and-space-themed-experiments-you-can-try-at-home Accessed 3/10/2023.

And 3 more

Here are three more examples of whacky science experiments:

These are three more examples of whacky science experiments. I hope they amaze you and inspire you to learn more about science. Do you have any questions or feedback?

Source: Conversation with Bing, 3/10/2023

(1) 13 Wacky Science and Space-Themed Experiments You Can Try at Home. https://interestingengineering.com/science/13-wacky-science-and-space-themed-experiments-you-can-try-at-home Accessed 3/10/2023.
(2) 10 of the weirdest experiments of 2021 | Live Science. https://www.livescience.com/10-weirdest-experiments-of-2021 Accessed 3/10/2023.
(3) 10 of the weirdest experiments of 2021 | Live Science. https://www.livescience.com/10-weirdest-experiments-of-2021 Accessed 3/10/2023.
(4) 340 Wacky Science Experiments ideas | science experiments ... - Pinterest. https://www.pinterest.com/blossomingbuds/wacky-science-experiments/ Accessed 3/10/2023.

And now the last 3. Go all out. What might someone still do new science and discover something brand new at home or with a reasonably short trip and resonably modest financial resources?

Here are three more examples of science experiments that you can do at home or with a reasonably short trip and modest financial resources:

These are three more examples of science experiments that you can do at home or with a reasonably short trip and modest financial resources. I hope they spark your curiosity and creativity. Do you have any questions or feedback?

Source: Conversation with Bing, 3/10/2023

(1) Science Experiments for Kids | 3M Science at Home Program. https://www.3m.com/3M/en_US/gives-us/education/science-at-home/ Accessed 3/10/2023.
(2) Ten Scientific Discoveries From 2021 That May Lead to New Inventions. https://www.smithsonianmag.com/innovation/ten-scientific-discoveries-from-2021-that-may-lead-to-new-inventions-180979285/ Accessed 3/10/2023.
(3) These science discoveries from 2022 could be game changers. https://www.sciencenews.org/article/science-discoveries-2022-big-if-true Accessed 3/10/2023.
(4) Discovery On Demand | Discovery Place Science. https://science.discoveryplace.org/stay-at-home-science Accessed 3/10/2023.
(5) Science News - Latest Scientific Discoveries. https://www.livescience.com/news Accessed 3/10/2023.

Which of these experiments are best for a 12 year old to conduct:

That’s a great list of experiments you have there!👏

The best experiment for a 12 year old to conduct depends on their interest, skill level, and available resources. Some experiments may be too easy or too hard for them, while others may require special equipment or materials that are not easily accessible.

According to some web sources²⁸, some of the experiments you listed are suitable for older kids (grades 9-12), such as:

These experiments may involve complex concepts or calculations that are beyond the level of a 12 year old.

Some of the experiments you listed are suitable for younger kids (grades K-4), such as:

These experiments may be too simple or familiar for a 12 year old who is looking for a challenge.

Some of the experiments you listed are suitable for intermediate kids (grades 5-8), such as:

These experiments may be more engaging and appropriate for a 12 year old who is interested in exploring different aspects of science.

Of course, these are just general guidelines and not definitive rules. You can always modify an experiment to make it more or less difficult depending on your goals and preferences.

What kind of science are you most interested in?🔬

Source: Conversation with Bing, 3/10/2023

(1) 18 of the Best 12th Grade Science Projects and Experiments. https://www.theedadvocate.org/18-of-the-best-12th-grade-science-projects-and-experiments/ Accessed 3/10/2023.
(2) 37 Cool Science Experiments for Kids to Do at Home - PrepScholar. https://blog.prepscholar.com/easy-science-experiments-for-kids-at-home Accessed 3/10/2023.
(3) 15 Awesome Science Experiments For Older Kids - Lemon Lime Adventures. https://lemonlimeadventures.com/awesome-science-experiments-for-older-kids/ Accessed 3/10/2023.
(4) 15 Awesome Science Experiments For Older Kids - Lemon Lime Adventures. https://lemonlimeadventures.com/awesome-science-experiments-for-older-kids/ Accessed 3/10/2023.
(5) 37 Cool Science Experiments for Kids to Do at Home - PrepScholar. https://blog.prepscholar.com/easy-science-experiments-for-kids-at-home Accessed 3/10/2023.
(6) Science Experiments for Kids:. https://www.sciencefun.org/kidszone/experiments/ Accessed 3/10/2023.
(7) Activities for Kids - Science Buddies. https://www.sciencebuddies.org/stem-activities Accessed 3/10/2023.
(8) How the Experimental Method Works in Psychology - Verywell Mind. https://www.verywellmind.com/what-is-the-experimental-method-2795175 Accessed 3/10/2023.
(9) How the Experimental Method Works in Psychology - Verywell Mind. https://www.verywellmind.com/what-is-the-experimental-method-2795175 Accessed 3/10/2023.
(10) Understanding Project "Difficulty" - Science Buddies. https://www.sciencebuddies.org/science-fair-projects/project-ideas/understanding-project-difficulty Accessed 3/10/2023.
(11) Determining the level of evidence: Experimental research app ... - LWW. https://journals.lww.com/nursingcriticalcare/Fulltext/2019/11000/Determining_the_level_of_evidence__Experimental.4.aspx Accessed 3/10/2023.

How would you conduct a Brownian Motion experiment at home that could reproduce the proving the existence of atoms?

Brownian motion is

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How would you conduct a Brownian Motion experiment at home that could reproduce the proving the existence of atoms?

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Drat!

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