Math Easy Solutions

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Math Easy Solutions

MES

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In this video I go over a quick review of the formulas for the scalar and vector projections of one vector onto another, as well as showing their visual representations. The scalar projection of a vector onto another vector is the magnitude of the projection and is visually seen as the adjacent side of a triangle. The vector projection is just the scalar projection multiplied by the unit vector along the vector being projected on. And as derived in my earlier video, the projects involve the dot product of the two vectors.

Timestamps:

- Question 7: Scalar and Vector Projections: 0:00
- Solution: Formulas: 0:08
- Visual representation: 0:55

Full video and playlists:

- Full video: https://youtu.be/VMKb69uDVt0
- HIVE notes: https://peakd.com/hive-128780/@mes/vectors-and-the-geometry-of-space-review
- Video sections playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0EMiATrjv8HH3fPwKVsgU6P
- Vectors and the Geometry of Space playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0FjJpwnxwdrOR7L8Ul8VZoZ .

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Join me as I explore the shape of the Earth. Is it round, flat, or a cube?

December 23, 2023 SATURDAY at 1 PM PST / 4 PM EST / 11 PM CAT

Stream notes and playlist:

- Stream notes and links: https://peakd.com/hive-128780/@mes/livestream-16-debunking-flat-earth
- MES Livestreams: https://www.youtube.com/playlist?list=PLai3U8-WIK0FqwyUa_ICwTlqO0S6Y3kAn
- All Livestreams: https://www.youtube.com/@mes/streams .

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The disclosure of free energy technology, as demonstrated to the world on 9/11, means the end of reality as we know it...

December 16, 2023 SATURDAY at 1 PM PST / 4 PM EST / 11 PM CAT

Stream notes and playlist:

- Stream notes and links: https://peakd.com/hive-128780/@mes/livestream-free-energy
- MES Livestreams: https://www.youtube.com/playlist?list=PLai3U8-WIK0FqwyUa_ICwTlqO0S6Y3kAn
- All Livestreams: https://www.youtube.com/@mes/streams .

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In this video I review the dot product formulas and its useful properties such as finding the angle between vectors and calculating work done on an object by a constant force. The dot product is the multiplication and addition of corresponding components of two vectors, producing a scalar. This result is also equal to the cosine of the angle between the vectors multiplied by their lengths. When the dot product is zero, the two vectors are perpendicular. Another useful property of the dot product is in projecting a vector onto another, which is useful in physics as a means of calculating work done by a constant force at a constant angle. There are many other applications of the dot product in physics, computer graphics, engineering, and machine learning. In fact, the dot product is fundamental in neural networks for measuring similarity between vectors.

Timestamps:

- Question 5: Dot product: 0:00
- Solution: Dot product from lengths and angle between vectors: 0:12
- Dot product from vector components: 1:19
- Question 6: Useful properties of dot products: 1:58
- Determining angle between 2 vectors: 2:09
- 2 vectors are orthogonal (perpendicular) if their dot product is zero: 3:03
- Projecting one vector onto another: 5:07
- Calculating work done by a constant force: 7:34
- Properties taken from ChatGPT: https://chatgpt.com/share/6e3be6a9-38d1-4ae7-852a-62977b6a492f: 9:21

Full video and playlists:

- Full video: https://youtu.be/VMKb69uDVt0
- HIVE notes: https://peakd.com/hive-128780/@mes/vectors-and-the-geometry-of-space-review
- Video sections playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0EMiATrjv8HH3fPwKVsgU6P
- Vectors and the Geometry of Space playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0FjJpwnxwdrOR7L8Ul8VZoZ .

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In #MESExperiments 39 I redo Viktor Schauberger's rising egg experiment but this time using an electric drill instead of manually stirring the water. This experiment confirms my earlier one, this time the plastic egg with the broad side up rose 21% faster and fell 24% slower than the ping pong ball. Note that the falling rate was similar to the 25% in the previous experiment, while the previous experiment the plastic egg with the broad side up rose 33% faster than the ping pong ball. The manual stirring in the previous experiment provided greater rotation speed of the water since all the objects rose faster in that experiment, thus likely also the affecting the percentage difference in rising rates. Nonetheless this further confirms Viktor Schauberger's experiment, and an egg shape with the broad side up rises faster in a water vortex than a spherical ping pong ball. Note that the ball and egg were filled with salt water (saline solution) so that they both have the same buoyancy.

Experiment results Viktor Schauberger links:

- Original unedited experiment: https://youtu.be/EwWh9VnAdWM
- Experiment results Excel file: https://1drv.ms/x/s!As32ynv0LoaIi4MMfqmCEPkIF58Hsg
- Living Energies book by Callum Coats: https://archive.org/details/LivingEnergies/page/n145/mode/2up?view=theater
- Rising egg experiment is on Page 141 (PDF 147)
- MES Local PDF: https://1drv.ms/b/s!As32ynv0LoaIiu9PhdOm-l40uNaTGA
- Experiment illustration: https://snipboard.io/8aOLe5.jpg
- Viktor Schauberger (30 June 1885 - 25 September 1958) wiki: https://en.wikipedia.org/wiki/Viktor_Schauberger
- Natural Philosophers wiki: https://wiki.naturalphilosophy.org/index.php?title=Viktor_Schauberger
- ChatGPT on Viktor Schauberger: https://chatgpt.com/share/b7d71c2a-1819-48b0-a183-928a6ee9698d
- Callum Coats wiki: https://wiki.naturalphilosophy.org/index.php?title=Callum_Coats

Timestamps:

- Replicating Viktor Schauberger's Rising Egg Experiment with a Drill: 0:00
- Ping pong ball weighs 28.46 g. Egg weighs 30.93 g 0:06
- Ping pong ball displaces 27 mL of water. Egg displaces 30 mL: 0:17
- Total Time of Rising and Falling: 0:32
- Experiment start: Ping pong ball vs Plastic egg (broad side down and up): 0:46
- Plastic egg with broadside down has fastest Total Time: 2:44
- Timing the Rising Only: 2:52
- Plastic egg with broadside up rose the fastest: 4:18
- Timing the Falling Only: 4:27
- Ping pong ball and plastic egg with broadside down fell the fastest (broadside up the slowest): 5:56
- Results: Plastic egg with broadside up rose 21% faster and fell 24% slower than the ping pong ball: 6:07
- Bar chart of the results: 6:21

Stay tuned for #MESExperiments 40...

Experiment screenshots and playlists:

- Screenshots of the Experiment: https://peakd.com/hive-128780/@mes/pyjcyzdu
- #MESExperiments video series: https://www.youtube.com/playlist?list=PLai3U8-WIK0HUHoank-Lj9q6RGAS51QRh
- Hive playlist: https://peakd.com/mesexperiments/@mes/list
- DRAFT #MESExperiments video series:

In this video I quickly review the vector between 2 points, which has a corresponding parallel vector from the origin called the position vector. The position vector is determined by subtracting the components between 2 points. Since the direction of the vector and magnitude of a vector governs most of its properties, the vector between 2 points is typically set to equal the position vector.

Timestamps:

- Question 4: Vector between two points: 0:00
- Solution: Position vector: 0:06
- Position vector is parallel to vector between two points: 0:44

Full video and playlists:

- Full video: https://youtu.be/VMKb69uDVt0
- HIVE notes: https://peakd.com/hive-128780/@mes/vectors-and-the-geometry-of-space-review
- Video sections playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0EMiATrjv8HH3fPwKVsgU6P
- Vectors and the Geometry of Space playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0FjJpwnxwdrOR7L8Ul8VZoZ .

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In this video I go over a quick review of the basics of vector algebra, namely the definitions of vectors vs scalars, and their addition or multiplication. A vector is a quantity that has both a magnitude and a direction (such as velocity), while a scalar just has a magnitude (such as temperature). We can add vectors by adding their components, and this is visually seen by placing one vector at the tip of another. Similarly, we can multiply a vector by a scalar by multiplying the scalar into each of the vector's components. Likewise, these basics extend to subtraction as well as vectors in 3D.

Timestamps:

- Question 1: Vector vs Scalar: 0:00
- Question 2: Vector addition: 0:39
- Solution: Adding vectors geometrically using Triangle or Parallelogram Law: 0:49
- Add vectors algebraically by adding components: 2:06
- Question 3: Multiplying vector by a scalar: 3:23
- Solution: Scalar shortens or extends a vector: 3:32
- Multiply a scalar into components of a vector: 4:04

Full video and playlists:

- Full video: https://youtu.be/VMKb69uDVt0
- HIVE notes: https://peakd.com/hive-128780/@mes/vectors-and-the-geometry-of-space-review
- Video sections playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0EMiATrjv8HH3fPwKVsgU6P
- Vectors and the Geometry of Space playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0FjJpwnxwdrOR7L8Ul8VZoZ .

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In this video I go over the end of chapter review questions covering the Vectors and the Geometry of Space chapter. There are 19 questions in total and serve as a good review on vectors, dot products, cross products, as well as the equations of lines, planes, and their applications. I also cover a few details, notably the distance between a point and a line, differently than I had in my earlier videos covering the chapter; so make sure to watch this video!

The topics covered as well as their timestamps are listed below.

- Intro: 0:00
- Calculus Book Reference: 0:58
- Sections in Calculus Book Chapter: 1:14
- Topics to Cover: 1:57
- Review: Concept Check: 19 Questions: 2:19
1. Question 1: Vector vs scalar: 2:54
2. Question 2: Vector addition: 3:33
3. Question 3: Multiplying vector by a scalar: 6:14
4. Question 4: Position vector: 7:45
5. Question 5: Dot product: 9:20
6. Question 6: Applications of dot product: 11:20
7. Question 7: Scalar and vector projections: 19:05
8. Question 8: Cross product: 21:02
9. Question 9: Applications of cross product: 27:33
10. Question 10: Parallelogram and Parallelepiped: 32:44
11. Question 11: Vector perpendicular to plane: 34:28
12. Question 12: Angle between 2 planes: 35:48
13. Question 13: Vector, parametric, and symmetric equations for a line: 37:04
14. Question 14: Vector and scalar equation for a plane: 40:46
15. Question 15: Parallel or perpendicular vectors and planes: 42:41
16. Question 16: Points on a line or plane: 46:22
- Solution to (a): 3 Points on a Line: 46:40
- Solution to (b): 4 Points on a Plane: 49:56
17. Question 17: Distances between Points, Lines, Planes: 52:08
- Solution to (a): Distance from a Point to a Line: 52:30
- Solution to (b): Distance from a Point to a Plane: 58:21
- Solution to (c): Distance between Two Lines: 1:00:00
18. Question 18: Traces of a surface: 1:14:50
19. Question 19: Six types of quadric surfaces: 1:21:58
- Outro: 1:26:53

Video notes and playlists:

- PDF notes: https://1drv.ms/b/s!As32ynv0LoaIi4Bu972HIENqNtdhRg
- HIVE notes: https://peakd.com/hive-128780/@mes/vectors-and-the-geometry-of-space-review
- Video sections playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0EMiATrjv8HH3fPwKVsgU6P
- Vectors and the Geometry of Space playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0FjJpwnxwdrOR7L8Ul8VZoZ .

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Allen Forrest joins the show again to discuss all things relating to Wilhelm Reich, Nikola Tesla, cosmic aether energy, and his personal experience with Reichian Therapy that has helped him realize his life's passion of being an artist and painter.

November 9 (SATURDAY) at 12 PM PST / 3 PM EST / 10 PM CAT

Allen Forrest's links:

- PeakD: https://peakd.com/@artgrafiken
- Dissident Voice: https://dissidentvoice.org/author/allenforrest
- Minds: https://www.minds.com/artgrafiken
- Odysee: https://odysee.com/@artgrafiken:f

Stream notes and playlist:

- Stream notes and links: https://peakd.com/hive-128780/@mes/livestream-15
- MES Livestreams: https://www.youtube.com/playlist?list=PLai3U8-WIK0FqwyUa_ICwTlqO0S6Y3kAn
- All Livestreams: https://www.youtube.com/@mes/streams

Related Videos:

MES Livestreams: https://www.youtube.com/@mes/streams .

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This stream is created with #PRISMLiveStudio

A simple explanation of what polynomials are and also how curves of various degrees of polynomials are shown as well as their relative patterns that arise.

Video notes and playlist:

- PDF: https://1drv.ms/b/s!As32ynv0LoaIiv8zPcr3nd8Z4b5IjA
- HIVE: https://peakd.com/hive-128780/@mes/polynomials-simple
- Math Basics playlist: https://www.youtube.com/playlist?list=PLE2F47766DE17B783

Related Videos:

Taylor Polynomials - Introduction and Derivation: http://youtu.be/p2EkXwkbflk
Polynomial Long Division - In depth Look on why it works!: http://youtu.be/E1H584xJS_Y
Polynomial Long Division - Examples: http://youtu.be/7XbzCQgqBPc
Factoring Quadratic Polynomials by Guessing: http://youtu.be/biEfGwT5pn4 .

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In this video I have made a compilation of many mysterious flashes that were present at the World Trade Center (WTC) on and surrounding the towers on 9/11. The flashes were present at several major events, such as during the 2nd "plane" strike, and the final dustification sequence of the North, South, and Building 7 Towers. A few buildings were the source of many flashes. The 32 Avenue of the Americas building had two "telecommunications masts" that were installed, along side emergency diesel generators, on the roof just days before September 11, 2001. Although these flashes are still a mystery, they nonetheless may help to unravel the inner workings of the cold directed energy weapon (DEW) used on to turn the towers mostly into dust.

These mystery flashes were brought to my awareness after Andrew Johnson shared an email from an anonymous individual pointing out these flashes out.

Original videos and more links:

- Anonymous email given to Andrew Johnson: https://www.checktheevidence.com/wordpress/2024/05/03/9-11-mysterious-flashes-at-the-wtc-complex/
- 9/11 Revisionist Substack article: https://911revision.substack.com/p/mysterious-flashes-at-the-wtc-complex
- 32 Avenue of the Americas building wiki: https://en.wikipedia.org/wiki/32_Avenue_of_the_Americas
- Building website: https://www.32-aofa.com/p/1
- Budco construction company: http://budco.us/jobs/32-avenue-of-the-americas
- Budco video: https://www.youtube.com/watch?v=YYnASmsj2mA
- Original videos with mystery flashes:
- At 1;43: https://www.youtube.com/watch?v=7hApRZ_7v2A
- At 10;50 and 2;27: https://www.youtube.com/watch?v=wRfphCLtUUI
- At 6;34 and 1;01: https://www.youtube.com/watch?v=yaydhlOVogk
- Building 7: https://www.youtube.com/watch?v=MBytxAhYL70

Timestamps:

- Mystery flashes on 9/11: 0:00
- Flashes behind WTC 2: 0:02
- Flashes on Dome: 0:07
- Flash on WTC 1 as 2nd "plane" strikes: 0:11
- Mystery formations (and flashes) on WTC 2 near earlier flash: 0:15
- Big flash on telecommunications mast: 0:35
- Flashes at multiple buildings: 0:42
- Flashes at multiple buildings as WTC 2 implodes into dust: 0:57
- Mystery formation at building flash site: 1:52
- 3 flashes in sync. Many flashes on and near telecommunications mast as South Tower falls: 2:07
- North Tower antenna blinking: 2:41
- Flashes at building as North Tower falls: 2:46
- 900 ft core columns "spire" turns to dust: 3:05
- Many more flashes at same building: 3:12
- Electromagnetic field interference in helicopter audio and video recording as WTC 1 falls: 3:43
- Flashes at telecommunications masts as North Tower implodes into dust: 3:53
- Spire turns to dust as flashes nearby: 4:18
- Blinking telecommunications mast as WTC 1 falls: 4:31
- Static interference in camera: 5:00
- Steel columns falling sideways into dust: 5:13
- Spire falling vertically downwards into dust: 5:35
- Flash at telecommunications mast right as Building 7 falls: 5:44
- More flashes at and near telecommunications mast: 5:50
- Two "t

In #MESExperiments 38 I show that stirring a column of water causes an egg to rise 33% faster and fall 25% slower than a ping pong ball, thus confirming Viktor Schauberger's rising egg experiment. Viktor Schauberger was an Austrian forester, inventor, and scientist that maintained the unique perspective that water was a living entity and prefers to move in a vortex manner. From this perspective, he stated that a shape that allows water to flow as a vortex around it would be able to move through water much easier than other shapes, such as a sphere. Viktor demonstrated this by his rising egg experiment, which involves stirring a column of water causing an egg to rise faster than a ping-pong ball filled with saline water to have the same buoyancy as the egg.

In order to validate his rising egg experiment properly, I used a plastic egg that was similar in size to a ping pong ball and filled them both with salt water until they sunk freely downwards. Then I performed the rising experiment 10 times each for the ping pong ball, the egg with broad side down, and the egg with broad side up. I timed the total time, and then I timed the rising only and falling only times. I did the experiment many times to minimize the influence of any variables such as stirring speed, water rotation rate, or position of the egg/ball in the cylinder.

At the start the egg fell faster than the ball indicating it was a bit more buoyant but, due to the water being in constant rotation after stirring, the egg with the broadside up fell 25% slower than the ping pong ball. In total, the egg with the broadside up rose 33% faster than the ping pong ball, while the egg with the broadside down still rose 18% faster than the PPB. Pretty amazing stuff!

Experiment results Viktor Schauberger links:

- Original unedited experiment: https://youtu.be/fcdZ2NipWNs
- Experiment results Excel file: https://1drv.ms/x/s!As32ynv0LoaIivgzFQ6k0XqICHrBiQ
- Living Energies book by Callum Coats: https://archive.org/details/LivingEnergies/page/n145/mode/2up?view=theater
- Rising egg experiment is on Page 141 (PDF 147)
- MES Local PDF: https://1drv.ms/b/s!As32ynv0LoaIiu9PhdOm-l40uNaTGA
- Experiment illustration: https://snipboard.io/8aOLe5.jpg
- Viktor Schauberger (30 June 1885 - 25 September 1958) wiki: https://en.wikipedia.org/wiki/Viktor_Schauberger
- Natural Philosophers wiki: https://wiki.naturalphilosophy.org/index.php?title=Viktor_Schauberger
- ChatGPT on Viktor Schauberger: https://chatgpt.com/share/b7d71c2a-1819-48b0-a183-928a6ee9698d
- Callum Coats wiki: https://wiki.naturalphilosophy.org/index.php?title=Callum_Coats

Timestamps:

- Replicating Viktor Schauberger's Rising Egg Experiment: 0:00
- Adding saline water to ping pong ball and plastic egg: 0:05
- Ping pong ball weighs 28.65 g. Egg weighs 31.29 g 0:18
- Total Time of Rising and Falling: 0:26
- Experiment start: Ping pong ball vs Plastic egg (broad side down and up): 0:33
- Plastic egg with broadside down has fastest Total Time

In this video I compare the conventional view of the Planck's constant as being merely a proportionality constant to solve the blackbody radiation problem vs FractalWoman's unique insight that Planck's constant may actually represent the minimum energy unit of ALL electromagnetic frequencies. In the conventional view, Max Planck's derived Planck's Law by assuming energy was quantized as E = n·h·f, where n is an integer number, h is Planck's constant, and f is the frequency of light. The issue here is the frequency has units of cycles per second, but the conventional formula ignores the cycles term. This makes the energy equation unbalanced since the units of energy will have a remaining cycle term.

By accounting for cycles via @FractalWoman's Modified Unit Analysis, it becomes apparent that the energy equation is actually a change in energy over time. This means that we need to balance out the equation by dividing by the cycles unit, which ultimately reinterprets Planck's constant as the energy per cycle. This is a grand simplification in the interpretation of light from "quantized frequencies" to "frequencies made up of quantized energy". I will be exploring this in the future, as it has far reaching implications for quantum physics.

FractalWoman links:

- FractalWoman's videos on Planck's constant: https://peakd.com/hive-128780/@mes/cycles-planck-s-constant-and-the-true-nature-of-light
- Modified Unit Analysis: https://youtu.be/xffcT_qMLxQ
- Planck's constant wiki: https://en.wikipedia.org/wiki/Planck_constant

Timestamps:

- MES Note on Planck's Constant: Quantum of action vs Quantum of energy: 0:00
- FractalWoman links and Planck's Law derivation: 0:43
- Planck's Law derivation involves quantizing energy as an integer multiplied by Planck's constant multiplied by frequency: 1:41
- Frequency of quantized energy gives rise to the concepts "Wave-particle duality" and "photons": 2:47
- FractalWoman aka Lori Gardi points out that frequency is in units "cycles per second": 3:50
- Account for cycles means Planck's constant is the unit of energy that makes up ALL frequencies: 4:15
- Figure showing 3 different wavelengths / frequencies of light per 1 unit of time: 5:25
- Frequency is not quantized but made up of many quanta of energy: 6:29

Full video and playlists:

- Full video: https://youtu.be/oJpwidXu9Ps
- HIVE notes: https://peakd.com/hive-128780/@mes/applied-project-radiation-from-the-stars
- Sections playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0H9KtXz4yi98pGrnnbSSYUb
- Sequences and Series Playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0EXHAJ3vRg0T_kKEyPah1Lz .

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In this video, I provide a quick review of the history behind Planck's Law, the formula derived by Max Planck in 1900 to resolve the Ultraviolet Catastrophe for blackbody radiation. The classical theory for blackbody radiation, proposed by John William Strutt (3rd Baron Rayleigh) and James Jeans, predicted that the energy emitted by a blackbody would increase without bound as the wavelength decreased, leading to a divergence at short wavelengths. This was wildly inaccurate, as experiments showed the energy spectrum peaks at a certain wavelength and then decreases at both higher and lower wavelengths.

Through a process of careful analysis, Max Planck derived a formula that matched experimental results by assuming that a hypothetical electrically charged oscillator in a cavity containing blackbody radiation can only emit energy in discrete quantities, or quanta. This was a significant departure from the previous theory of continuous energy intervals. Planck's revolutionary assumption of quantized energy emission pioneered the development of modern quantum mechanics.

Timestamps:

- Planck's Law describes spectral density of electromagnetic radiation of a black body at thermal equilibrium: 0:00
- 1900, Max Planck proved that a hypothetical electrically charged oscillator can only change its energy in increments: 0:51
- The Law: Spectral emissive power per unit area, per unit solid angle for particular radiation frequencies: 1:48
- Increasing temperature increases total radiated energy and peaks at shorter wavelengths: 2:21
- Planck's Law formula: 2:41
- Graph of Comparison between Planck's Law vs Classical Theory (Rayleigh-Jeans Law): 3:34
- Solid angle (units in steradians) is angle of projection for a specific area on the surface of a sphere: 4:16
- Solid angle is used to quantify amount of radiation projected from a heat source: 4:49
- Note that Wikipedia uses various versions of Planck's Law: 5:18
- Rayleigh-Jeans Law formula (classical theory): 5:34
- Rayleigh-Jeans Law formula in terms of frequency: 6:22
- Ultraviolet Catastrophe: Rayleigh Jeans-Law strongly disagrees at short wavelengths: 6:43
- Planck's Law formula as energy density: 7:17
- Planck's Law and Rayleigh-Jeans Law formulas (used in my Calculus book): 7:44
- Planck's Law and Rayleigh-Jeans Law formulas as energy density in terms of frequency: 8:32

Full video and playlists:

- Full video: https://youtu.be/oJpwidXu9Ps
- HIVE notes: https://peakd.com/hive-128780/@mes/applied-project-radiation-from-the-stars
- Sections playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0H9KtXz4yi98pGrnnbSSYUb
- Sequences and Series Playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0EXHAJ3vRg0T_kKEyPah1Lz .

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In this video I graph out the blackbody radiation energy density for the Sun using both Planck's Law and the classical Rayleigh-Jeans Law. At high wavelengths, both models are similar but at low wavelengths the classical theory diverges wildly to infinity. This was the cause of the Ultraviolet Catastrophe. Planck's Law accurately models experiment data which shows a peak energy density at the 0.5 um wavelength for the Sun, whose temperature is 5700 Kelvin.

Timestamps:

- Question 3: Graphing Planck's Law and Rayleigh-Jeans Law for the Sun (5700 K): 0:00
- Solution to Question 3: Converting meters to micrometers for wavelength: 0:52
- Graphing in Excel: Energy Density (energy volume per each wavelength) vs wavelength: 1:33
- Planck's Law and Rayleigh-Jeans Law are similar at large wavelengths: 2:22
- Planck's Law and Rayleigh-Jeans Law are very different at small wavelengths: 2:51
- Comparison Summary: Ultraviolet Catastrophe: 3:12
- Planck's Law give a maximum at a wavelength of 0.5 um, Rayleigh-Jeans Law has no maximum or minimum: 4:20
- Question 4: Planck's Law for the Sun gives a maximum at a wavelength of 0.5 um: 5:01

Full video and playlists:

- Full video: https://youtu.be/oJpwidXu9Ps
- HIVE notes: https://peakd.com/hive-128780/@mes/applied-project-radiation-from-the-stars
- Sections playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0H9KtXz4yi98pGrnnbSSYUb
- Sequences and Series Playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0EXHAJ3vRg0T_kKEyPah1Lz .

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In this video I show that using just the first term for the Taylor series expansion of the exponential function in Planck's Law, it becomes Rayleigh-Jeans Law. This results in a good approximation for Rayleigh-Jeans Law at large wavelengths since the extra terms of the Taylor series become very small.

Timestamps:

- Question 2: Using Taylor polynomials, Planck's Law approximates Rayleigh-Jeans Law at large wavelengths: 0:00
- Solution: Approximating exponential function using Taylor series: 0:28
- Recap on Taylor series: 0:56
- Exponential function as a Taylor series: 2:40
- Approximating Planck's Law using Taylor series for Exponential function: 4:03
- Approximating Taylor series for large wavelengths: 5:58
- Large wavelength approximation for Planck's Law: 6:40
- Canceling out terms of Planck's Law to get Rayleigh-Jeans Law: 8:36
- Summary: Using the first non-zero term of Taylor series only approximates Rayleigh-Jeans Law: 9:44

Full video and playlists:

- Full video: https://youtu.be/oJpwidXu9Ps
- HIVE notes: https://peakd.com/hive-128780/@mes/applied-project-radiation-from-the-stars
- Sections playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0H9KtXz4yi98pGrnnbSSYUb
- Sequences and Series Playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0EXHAJ3vRg0T_kKEyPah1Lz .

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Join me as I dive deep into the missing Malaysia Airlines Flight 370 (MH370) plane, and explore the more esoteric, predictive programming, and downright eerie circumstances regarding this Psychological Operation (and indeed it is a PsyOp).

TODAY at 1 PM PST / 4 PM EST / 11 PM CAT

Stream notes and playlist:

- Stream notes and links: https://peakd.com/hive-106474/@mes/livestream-13
- MES Livestreams: https://www.youtube.com/playlist?list=PLai3U8-WIK0FqwyUa_ICwTlqO0S6Y3kAn
- All Livestreams: https://www.youtube.com/@mes/streams .

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In this video I show by using l'Hospital's Rule for indeterminate limits, that Planck's Law for blackbody radiation approaches zero as the wavelength approaches zero or infinity. Trying to take the limits directly obtains an indeterminate result (either 0/0 or ∞/ ∞), which means we can apply l'Hospital's Rule and use the derivative of the numerator and denominator for the limit. In the case for the limit as wavelength approaches 0, we have to apply l'Hospital's Rule multiple time since several iterations of l'Hospital's Rule still obtain an indeterminate result of the form ∞/∞. Fortunately, a pattern arises in that each iteration obtains the same result as the previous one but with one less lambda (λ) or wavelength term. After 4 iterations of the l'Hospital's Rule, we find that the limit is in fact zero, thus also solving the ultraviolet catastrophe arising from the previous Rayleigh-Jeans Law which approached infinity at small wavelengths.

Timestamps:

- Question 1: Limits of Planck's Law using l'Hospital's Rule: 0:00
- Solution: Recap on l'Hospital's Rule for indeterminate limits: 0:28
- Grouping constants together in Planck's Law: 2:23
- Limit as wavelength approaches zero is indeterminate (∞/∞): 4:51
- Limit as wavelength approaches infinity is indeterminate (0/0): 6:36
- Applying l'Hospital's Rule for the limit at infinity: 7:55
- Limit of Planck's Law as wavelength approaches infinity is equal to zero: 15:02
- Applying l'Hospital's Rule for the limit at zero is still indeterminate (infinity / infinity): 15:33
- Applying 2nd iteration of l'Hospital's Rule for limit at zero is still indeterminate (infinity / infinity): 17:00
- Pattern shows that applying l'Hospital's Rule 3 more times the limit becomes zero: 21:23
- Limit of Planck's Law as wavelength approaches zero is equal to zero: 24:20

Full video and playlists:

- Full video: https://youtu.be/oJpwidXu9Ps
- HIVE notes: https://peakd.com/hive-128780/@mes/applied-project-radiation-from-the-stars
- Sections playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0H9KtXz4yi98pGrnnbSSYUb
- Sequences and Series Playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0EXHAJ3vRg0T_kKEyPah1Lz .

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This video walks through several types of power functions and shows the symmetry and patterns that arise from graphing them.

Video notes and playlist:

- PDF: https://1drv.ms/b/s!As32ynv0LoaIivcChAz6-Tm9z8gJMg
- HIVE: https://peakd.com/hive-128780/@mes/power-functions-part-3-graphing
- Power Functions playlist: https://peakd.com/hive-128780/@mes/power-functions-part-3-graphing

Related Videos:

Power Functions Part 1: http://youtu.be/2MKko4ZkSf0
Power Functions Part 2: http://youtu.be/VzFUDiLzRiE .

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In this video I have made a compilation of all known footage of the famous iron block Hutchison Effect experiment (including a RARE earlier experiment) in which a 2"x2"x7" solid iron block shrivels, warps, and twists as if it was made of jelly. John Hutchison performed these 2 experiments in Los Angeles, USA, in November 2008. The rare earlier experiment used a very low quality camera, but the second famous experiment used a professional camera. However, the only footage I have available are from the YouTube uploads. I am currently in talks with John and his wife Nancy in hopes of finding the raw original high quality footage and photos of both experiments.

The iron block experiment is very clear video evidence that the Hutchison Effect is very very real. "Debunkers" can't resort to the usual video fakery slander, but instead make bogus claims that the solid piece of iron metal was actually "plastic" or "foam" or "clay", and some sort of "heat gun" was being used. These slanderous lies are easily debunked just by watching the compilation, as it shows no evidence heat, and John literally places a magnet on both the iron block and the iron flakes that fell of it.

John Hutchison had sold the iron block on eBay many years ago and I am also helping him pinpoint who has it now. Stay tuned!

Original videos (in order):

- John Hutchison's old channel: https://www.youtube.com/@HUTCHISONEFFECT2009
- VANISHING STEEL: https://youtu.be/eWEx1_xpSP0
- Second iron block experiment:
- UFO SPOTED: https://youtu.be/xSjdaJgOsfc
- UFO GRAVITY: https://youtu.be/sZa9Y7nVCJQ
- HUGE UFO INVASION: https://youtu.be/hGA0DzQaFtM
- UFO CRASH SITE: https://youtu.be/3PY-lXStdUo
- METAL DISRUPTION: https://youtu.be/UnfmwqnpxsM
- GRAVITY EFFECTS RF: https://youtu.be/fcGJXJuvrso
- GRAVITY EFFECTS: https://youtu.be/_Rb7OG9kC7k
- METAL DISRUPTION 2008: https://youtu.be/0gR0lX63_ZY
- JELLY IRON BLOCK: https://youtu.be/rTPmDB0uVKA
- First iron block experiment:
- IRON BLOCK JELLY: https://youtu.be/F2gT0LibBHU
- DISINTEGRATED STEEL BLOCK: https://youtu.be/pW0llWO2gcg
- Picture CLOSE UP: https://youtu.be/WHBN0J2qw6w
- ALIEN METALS: https://youtu.be/121-2jI9qvM

Timestamps:

- November 3, 2008: John Hutchison moving 2"x2"x7" cast iron block in place: 0: 0:00
- 2nd iron block experiment (better quality): 2:33
- Iron block starts warping and twisting: 3:16
- Iron block starts "fuming": 3:23
- John takes iron block out of test area and zooms in: 3:37
- John says the sample was cold, and smoke may be dust: 4:41
- November 20, 2008: Plastic hollow ball lifted by static electricity while iron block is in background: 5:12
- Flakes of the iron block zoomed in: 5:39
- Magnet on iron block and iron flakes / filings: 7:23
- Not shown in video, John said the iron flakes were strangely magnetic and spun around: 7:39
- 1st iron block experiment (lower quality): 8:28
- Iron block starts to shrivel: 8:40
- Camera cuts off and John says a pulse knocked out the camera as i

In this video I provide an overview of blackbody radiation, which is an object that absorbs all radiation and emits radiation that is dependent only on its temperature, as well as discussing the mathematical models used to describe it. In the 19th century, Rayleigh-Jeans Law was used to model blackbody radiation but it predicted that the energy density of the blackbody would go to infinity as wavelength goes to zero. In reality, experiments showed the opposite and that the energy density goes to zero as well. Then in 1900, Max Planck provided a more accurate model, termed Planck's Law, which considered light as being composed of discrete packets or "photons", and hence was able to resolve this problem in physics. This event was termed the Ultraviolet Catastrophe.

Timestamps:

- Blackbody absorbs all radiation and emits radiation dependent only on temperature: 0:00
- Blackbody approximation: Small hole in a hollow object: 0:28
- Color temperature of a black-body radiator: 1:05
- Blackbody radiation depends on temperature only, not shape: 1:19
- Table of color and temperature for blackbody radiation: 1:48
- Blackbody radiation spectral radiancy vs wavelength: 2:29
- The Sun and stars are close to being blackbodies: 3:15
- Wavelength is length of waves. Frequency is waves per second: 3:51
- Rayleigh-Jeans Law (19th century) for blackbody energy density: 4:20
- Boltzmann's constant relates kinetic energy to temperature of a gas, or electromagnetic waves: 4:47
- Kelvin (K) is base unit of temperature for International System of Units (SI): 5:22
- Water freezes at 273.15 K = 0 C = 32 F and boils at 373.15 K = 100 C = 212 F: 5:30
- Difference between water boiling and freezing is 100 K or 100 C or 180 F: 5:49
- Absolute zero, 0 K, is assumed lowest motion of ideal gases (no spatial dimension and don't have interparticle attraction or repulsion): 6:06
- Ultraviolet Catastrophe: Rayleigh-Jeans Law is inaccurate for shorter frequencies: 6:37
- Planck's Law (1900) is a better model for blackbody radiation: 7:17
- Planck's constant is the "quantum of action" and is multiplied by a photon's frequency to get its energy: 8:24

Full video and playlists:

- Full video: https://youtu.be/oJpwidXu9Ps
- HIVE notes: https://peakd.com/hive-128780/@mes/applied-project-radiation-from-the-stars
- Sections playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0H9KtXz4yi98pGrnnbSSYUb
- Sequences and Series Playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0EXHAJ3vRg0T_kKEyPah1Lz .

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In this video I go over a brief introduction into cell theory, which states that all living things are composed of one or more cells, and in multicellular organisms, every cell is derived from a single cell inside a fertilized egg. More terms and definitions covered are listed below.

Timestamps:

- Cell theory states all living things are composed of one or more cells: 0:00
- Eukaryotic cells contain a nucleus and can be single-celled or multicellular. Prokaryotic cells are single-celled and do not contain a nucleus: 0:56
- Every cell in a multicellular organism is derived from a single cell in a fertilized egg: 1:22
- Fertilization or impregnation is the fusion of gametes to give rise to a new organism: 1:30
- Sexual reproduction is the cycle of fertilization: 1:54
- Insemination is the introduction of sperm into a female's reproductive system: 1:59
- Pollination is the transfer of pollen (which produce gametes) from a male part of a plant to a female part: 2:06
- Gamete or sex cell is a haploid cell that fuses with another haploid cell during fertilization: 2:23
- Female is any individual that produces the larger type of gamete (ovum) and a male produces the smaller type (sperm): 2:38
- Sperm and ovum fusing: 2:57
- Ploidy is number of complete sets of chromosomes in a cell: 3:00
- Sets of chromosomes refer to the number of maternal and paternal chromosome copies in each homologous chromosome pair: 3:13
- Somatic (non-sex) cells, tissues, individual organisms: Ploidy level: monoploid (1 set), diploid (2 sets), triploid (3 set), etc.: 3:48
- Polyploid refers to 3+ chromosome sets: 4:50
- Homologous chromosomes or homologs are a set of one maternal and paternal chromosome that pair up during fertilization: 4:59
- Haploid has 1 complete set of chromosomes for a diploid species; 2 sets for a tetraploid species: 5:27
- Haploid cells in humans have 23 chromosomes; diploid cells have 46 chromosomes: 6:20
- Haploid has 2 related definitions: a cell with half the number of chromosomes in somatic cells, and a cell with just 1 set of chromosomes, termed monoploid: 7:08
- Zygote is a eukaryotic cell formed by a fertilization event between 2 gametes: 7:33
- Zygote's genome is a combination of the DNA of each gamete: 7:44
- Egg results from fertilization of an egg cell and contains the zygote from which an embryo develops: 7:53
- Embryo is the early stage of development of a multicellular organism: 8:10
- Fetus refers to 9+ weeks after conception in humans: 8:15
- Male human embryo of 7 weeks old or 9 weeks gestational age: 8:38
- Gestational age starts from the woman's last menstrual period (LMP): 8:38
- Menstruation or period is regular discharge of blood and mucosal tissue from the uterus through the vagina: 9:02
- Mucous membrane or mucosa is a membrane that lines various cavities in the body and covers internal organs: 9:28
- Uterus or womb is where the fetus develops during gestation: 9:37
- Gestation is period of development during the carrying of t

In this video I go over the properties and structures of the 4 main types of macromolecules (or very large molecules) that are found in all living organisms: proteins, polysaccharides, nucleic acids, and lipids. The first 3 (proteins, polysaccharides, nucleic acids) are formed from smaller repeating units called monomers. On the other hand, lipids are not defined by any chemical structure and represent a broad group of organic compounds such as fats, phospholipids, and steroids. More terms and definitions are listed in the timestamps below.

Timestamps:

- Macromolecules or very large molecules: 0:00
- Table of 4 major macromolecules: proteins, nucleic acids, polysaccharides, lipids: 0:56
- Specialized roles of macromolecules in cells: 3:44
- Lipids are only class of macromolecules not made up of polymers (not composed of smaller repeating monomers): 4:08
- Phospholipids or phosphatides are lipids with a hydrophilic head containing a phosphate and 2 hydrophobic tails derived from fatty acids: 4:21
- Phospholipid forming cell membrane bilayer: 4:56
- Lumen is inside space of a tubular structure: 5:30
- Steroid is a lipid with four rings and is biologically active: 5:37
- Cholestane steroid structure: 6:00
- Membrane fluidity is the viscosity of the lipid bilayer of a cell membrane: 6:28
- 3 main structures of phospholipids: liposome, micelle, bilayer sheet: 7:09
- Proteins are most diverse macromolecules. Nucleic acids handle hereditary information: 7:51
- Antibody (Ab) or immunoglobulin (Ig) are Y-shaped proteins that attack foreign objects: 8:11
- Antigen is unique molecule of the pathogen which the antibody recognizes: 8:35
- Antibody-antigen binding site via lock and key theory: 9:16
- Primary, secondary, tertiary, quaternary structures of a hemoglobin protein: 9:56
- Hemoglobin (Hb or Hgb) contains iron and transports oxygen in the red blood cells: 12:32
- Red blood cells (RBCs) or red cells or erythrocytes are main means of delivering oxygen to the body tissues: 12:42
- Biomolecular structure is the folded, 3D shape formed by a molecule of protein, DNA, or RNA: 13:29
- Protein complex is a group of 2 or more polypeptide chains and are form of quaternary structure: 14:02
- 4 main scales of molecular structure: primary, secondary, tertiary, and quaternary: 14:37
- Scaffold or support for the biomolecular structure arises from the hydrogen bonds at the secondary level: 14:47
- Diagram of 4 levels of structure for proteins and nucleic acids: 15:14
- Histones are proteins that act as spools for DNA to wrap around it forming structural units called nucleosomes: 17:10

Full video below:

- #MESScience 3: Overview of Biology: https://youtu.be/WX_qzT0nZFY
- HIVE video notes: https://peakd.com/hive-128780/@mes/messcience-3-overview-of-biology
- Video sections playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0FYO6bxFbBAtVJ9sDOJnH72
- #MESScience playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0FjJpwnxwdrOR7L8Ul8VZoZ .

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In this video I provide an overview of the essential molecules found in all life forms on Earth, namely the nucleotides DNA and RNA as well as their precursor and "energy currency" ATP. The terms covered and their definitions are listed in the timestamps.

Timestamps:

- Nucleotides consist of a nucleoside and phosphate: 0:00
- Polynucleotide is composed of 13 or more nucleotides: 0:34
- Phosphoric acid is a weak acid with formula H3PO4: 1:42
- Phosphate is an anion, salt, functional group or ester of phosphoric acid: 2:22
- Inorganic phosphate are free phosphate anions in solution and denoted Pi: 3:53
- Nucleoside consists of a nucleobase and a 5-carbon sugar (Ribose or Deoxyribose): 4:22
- Ribose has 1 more oxygen than deoxyribose: 4:35
- Deoxy sugars have a hydroxyl -OH group replaced with hydrogen H (deoxy = loss of an O): 4:46
- Nucleobases or nitrogenous bases or bases contain nitrogen and can form nucleosides and base pairs: 6:35
- 5 primary nucleobases: adenine (A), cytosine (C), guanine (G), thymine (T), uracil (U): 7:18
- Purines (A, G) are fused-ring nucleobases: 8:12
- Pyrimidines (C, T, U) are simple ring nucleobases: 8:22
- Base pair (bp) consists of 2 nucleobases bound by hydrogen bonds: 9:03
- Complementarity is the property of base pairing in reverse mirroring order (anti-parallel): 10:36
- Purines can only base pair with pyrimidines, and vice versa: 11:09
- DNA base pairing: A-T, and G-C. RNA base pairing: A-U, and G-C: 13:30
- A-T DNA base pair via 2 hydrogen bonds: 14:35
- G-C DNA and RNA base pair via 3 hydrogen bonds: 14:49
- A-U RNA base pair via 2 hydrogen bonds: 15:01
- Nucleic acids are composed of nucleotides (main classes are DNA and RNA): 15:32
- Diagram of RNA and DNA: 16:51
- Deoxyribonucleic acid (DNA) is composed of 2 polynucleotide chains in a double helix: 18:01
- 98% of DNA in humans are non-coding (aren't patterns for protein sequences): 18:31
- Structure of the DNA double helix: 18:45
- Location of eukaryote nuclear DNA: 20:34
- Ribonucleic acid (RNA) is typically made of 1 polynucleotide chain: 22:00
- Hairpin loop of RNA folded onto itself: 22:47
- Nucleic acid sequence is a succession of bases indicating the order of nucleotides: 23:28
- Sequences usually presented form 5' end to 3' end: 24:21
- DNA and RNA are synthesized in the 5' to 3' direction: 25:25
- Polymerase is an enzyme that synthesizes long chains of polymers or nucleic acids: 26:24
- Enzymes are proteins that accelerate chemical reactions: 26:28
- Phosphodiester bond is when two hydroxyl groups in phosphoric acid react with hydroxyl groups on other molecules to form 2 ester bonds: 27:15
- Diagram of phosphodiester bonds between 3 nucleotides: 29:09
- Structural elements of 3 nucleotides: 30:30
- Glycosidic bond is a covalent bond that joins a sugar molecule to another group: 32:45
- Phosphate-deoxyribose backbone DNA segment shown from 5' to 3' end: 33:21
- DNA sequence is written form the 5' to 3' end for the Top strand and 3' to 5' for

In this video I go over amino acids, which are derived from ammonia and carboxylate, and combine together to form peptides or longer chains as proteins. Amino acids combine via peptide bonds, which are covalent bonds that involve the loss of a water molecule. Thus, technically, peptides and proteins are made up of amino acid residues, indicating they are formed from the "residue" or leftover molecules in the peptide bond reaction (since water is lost). Further terms and definitions are listed in the timestamps below.

Timestamps:

- Ammonia (NH3) is a compound of nitrogen and hydrogen: 0:00
- Amines have a basic nitrogen atom with a lone pair of electrons: 1:09
- Amino group is the substituent -NH2: 2:25
- Amino acids contained charged amino (ammonio), carboxylate, and a side chain: 3:05
- Every amino acid contains carbon, hydrogen, oxygen, nitrogen: 4:20
- Structure of generic L-amino acid used for systematic naming: 4:45
- L- vs D- amino acids are left and right handed (chiral) configurations: 5:21
- A molecule or ion is chiral if it can't be superposed on its mirror image by any combination of rotations, translation, some conformational changes: 6:30
- A chiral molecule or ion exists in 2 stereoisomers that are mirror images, called enantiomers: 7:14
- Peptides are short chains of amino acids linked by peptide bonds (covalent bond that releases a water molecule): 8:36
- Oligopeptide consists of 2 to 20 amino acids: 9:44
- Polypeptide is a longer continuous unbranched peptide chain: 10:08
- Protein is a polypeptide with more than approximately 50 amino acids: 10:22
- Proteins consists of 1+ polypeptides arranged in a biologically functional way: 11:09
- Ligand forms a complex (surrounding a central atom or ion) with a biomolecule: 11:39
- Cofactor is required for an enzyme's activity as a catalyst (increases rate of reaction): 13:08
- Amino acid residues refer to the amino acids left over from peptide bonds which removes a water molecule: 13:51
- Condensation reaction combines two molecules into one: 15:54
- Protein sequence is the linear sequence of amino acids, reported from amino-terminal (N) end to carboxyl-terminal (C) end: 16:02

Full video below:

- #MESScience 3: Overview of Biology: https://youtu.be/WX_qzT0nZFY
- HIVE video notes: https://peakd.com/hive-128780/@mes/messcience-3-overview-of-biology
- Video sections playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0FYO6bxFbBAtVJ9sDOJnH72
- #MESScience playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0FjJpwnxwdrOR7L8Ul8VZoZ .

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Created 6 years, 10 months ago.

1300 videos

Category Education

I mainly teach math, but also make "controversial" videos that are censored on YouTube, as well as creating #FreeEnergy technology!