Cursed Units
TLDRThe video script explores the intriguing world of unusual scientific units, highlighting the humor and complexity behind them. It delves into examples such as Randall Monroe's 'What If' article, where peculiar calculations lead to unexpected unit cancellations, like 'poops per bird per hour' and the concept of fuel efficiency in different regions. The script also discusses more abstract units like kilowatt-hours and their physical interpretations, emphasizing the importance of dimensional analysis in understanding physical constants and equations. It further examines the Hubble constant and its implications for the universe's age, as well as the concept of negative and fractional powers in units, exemplified by 'picoseconds per square root kilometre' in the context of polarisation mode dispersion in optical fibers. The video concludes by inviting viewers to share their own experiences with 'cursed' units, celebrating the oddities and challenges of scientific measurement.
Takeaways
- π The website 'What If' by Randall Monroe addresses absurd hypothetical questions with scientific precision.
- π¦ The likelihood of a bird dropping in your mouth while lying on your back isζδ½, estimated at 195 years.
- π£οΈ Unit cancellation is a strange phenomenon where units seemingly cancel out to give a simple figure, as seen in gas mileage calculations.
- π Gas mileage is measured differently in the US (miles per gallon) and in Europe/Australia (litres per 100 km), leading to interesting unit conversions.
- π The concept of fuel efficiency can be visualized as the cross-sectional area of a fuel tube that maintains tank level while driving.
- π Kilowatt hours are a 'cursed' unit that combines energy divided by time, multiplied by time, resulting in a complex unit of energy.
- π Dimensional analysis uses units in equations to verify the correctness of those equations, as demonstrated by the gravitational constant's units.
- π The Hubble constant, measured in kilometres per second per megaparsec, describes the rate of the universe's expansion and has an interesting relationship with the age of the universe.
- π The units of the Hubble constant can be converted to inverse seconds, which coincidentally is close to the estimated age of the universe.
- π Polarisation mode dispersion (PMD) is a complex unit that arises from the different speeds of light for different polarisations in optical fibres, measured in picoseconds per βkm.
- 𧬠The study of DNA and polymers can also lead to 'cursed' units, such as nanometres per βnm, due to the random walk nature of their structure.
- π€ The video script highlights the beauty and awkwardness of mathematics and science, showcasing the range of experiences from elegant to inexplicably complex.
Q & A
What is the website 'What If' and who is behind it?
-The website 'What If' is a platform where cartoonist and engineer Randall Monroe answers hypothetical questions with scientific detail. It is known for its humorous and precise approach to answering absurd scenarios.
How long would one have to wait for a bird to poop in their mouth if they lay down on their back with their mouth open?
-According to Randall Monroe's calculations, one would have to wait approximately 195 years for a bird to poop in their mouth under such circumstances.
What is the strange unit cancellation observed in fuel efficiency measurements?
-The strange unit cancellation in fuel efficiency measurements is observed when comparing the US measurement of miles per gallon to the European and Australian measurement of litres per 100 kilometres. Both units, when broken down, cancel out to a square millimetre unit, which is an unusual and unexpected result.
What is the physical interpretation of fuel efficiency in terms of a thin tube of fuel?
-The physical interpretation of fuel efficiency is imagining a thin tube of fuel running alongside your vehicle, feeding into the fuel tank. Your gas mileage corresponds to the precise cross-sectional area of this tube that keeps the fuel level in your tank constant as you drive.
What are kilowatt hours and why are they considered cursed units?
-Kilowatt hours are a unit of energy, representing the power consumption of a device running at a rate of one kilowatt for one hour. They are considered cursed units because they result from multiplying power by time, leading to a unit that is difficult to intuitively understand or visualize, especially when compared to simpler units like miles per gallon or metres per second.
How does dimensional analysis help in understanding physical equations?
-Dimensional analysis is a method that involves looking only at the units in an equation. It helps verify the correctness of the equation by ensuring that the units on both sides of the equation match up. This technique can also guide the derivation of the correct form of an equation when dealing with physical constants and their associated units.
What is the Hubble constant and how is it measured?
-The Hubble constant is a measure of the rate of expansion of the universe. It is measured by observing distant galaxies and noting their velocity and distance from us. The constant is expressed in kilometres per second per megaparsec, and it describes how fast galaxies are moving away from us based on their distance.
Why are parsecs used as a unit of measurement for astronomical distances?
-Parsecs are used for astronomical distances because they directly relate to the method of measuring distances to faraway objects using trigonometry and the positions of Earth in its orbit around the Sun. A parsec is defined by the angle that an object appears to shift against the background stars when viewed from two points separated by one astronomical unit (the distance between Earth and the Sun).
What is the significance of the Hubble constant's value in inverse seconds?
-When the Hubble constant is expressed in inverse seconds (Hz), it provides a rough approximation of the age of the universe. The number obtained from this conversion is close to the estimated age of the universe, which is approximately 13.7 billion years. However, this is a coincidence, as the actual age of the universe is not derived from the Hubble constant in a straightforward manner.
How does the concept of a random walk relate to polarisation mode dispersion (PMD) in optical fibres?
-Polarisation mode dispersion (PMD) in optical fibres is related to the concept of a random walk through the presence of random impurities in the fibre that cause different polarisations of light to travel at slightly different speeds. This variation leads to a dispersion effect that increases with the square root of the fibre's length, similar to how a random walk's distance from the starting point increases with the square root of the number of steps taken.
What is the significance of units with fractional or irrational powers in scientific measurements?
-Units with fractional or irrational powers can arise when describing relationships that follow complex power laws. These units reflect the mathematical properties of the relationships being measured and can provide insight into the behavior of physical phenomena, even though they may be less intuitive or more difficult to understand than units with whole number exponents.
How does the speed of light vary inside a substance like glass compared to a vacuum?
-The speed of light slows down when it travels through a substance like glass compared to its speed in a vacuum. This variation is due to the properties of the material, such as its refractive index, which affects how light waves interact with the material's atoms and molecules.
Outlines
π€ The Curious Case of Unusual Units
This paragraph introduces the concept of unusual or 'cursed' units in science, exemplified by the hypothetical scenario of waiting for a bird to poop in one's mouth and the peculiarities of fuel efficiency measurements. It discusses how Randall Monroe's 'What If?' website tackles such hypothetical questions with scientific rigor, and how everyday units like miles per gallon and liters per 100 kilometers have strange underlying cancellations of volume and distance. The speaker also shares personal experiences with cursed units during undergraduate studies, setting the stage for a deeper exploration of the topic.
π Cosmic Distances and the Hubble Constant
The second paragraph delves into the complexities of measuring cosmic distances and introduces the Hubble constant, a measure of the universe's expansion rate. It explains the historical context of the Hubble constant's discovery and the method of determining distances to distant galaxies using parallax and the definition of a parsec. The paragraph also discusses the calculation of the Hubble constant in kilometers per second per megaparsec and its peculiar units, leading to a fascinating conversion into inverse seconds that hints at the age of the universe.
π Understanding the Hubble Constant's Implications
This paragraph further explores the implications of the Hubble constant, clarifying misconceptions about the uniform expansion of the universe and the actual age of the universe compared to the Hubble time. It emphasizes the Hubble constant's role as a parameter rather than a constant over time, and the intriguing coincidence of the Hubble time being close to the age of the universe. The speaker also reflects on the challenges of interpreting units with irrational or fractional exponents, highlighting the importance of context in scientific measurements.
𧬠The Random Walk of Scientific Units
The final paragraph discusses the concept of random walks in scientific measurements, particularly in the context of polarisation mode dispersion in optical fibers and the scattering measure in pulsar scintillation research. It explains how the presence of impurities in materials can lead to different speeds for different polarisations of light, resulting in dispersion measured in unconventional units like picoseconds per square root kilometer. The speaker also shares a personal anecdote about researching DNA molecule behavior, culminating in the mention of the 'most cursed unit' encountered: nanometers per square root nanometer. The paragraph concludes with an invitation for viewers to share their experiences with unusual scientific units.
Mindmap
Keywords
π‘Randall Monroe
π‘Unit Cancellation
π‘Fuel Efficiency
π‘Kilowatt Hours
π‘Dimensional Analysis
π‘Gravitational Constant
π‘Hubble Constant
π‘Parsec
π‘Redshift
π‘Polarisation Mode Dispersion (PMD)
π‘Random Walk
Highlights
Randall Monroe's website 'What If' answers absurd hypothetical questions with scientific precision.
The question of how long one would have to wait for a bird to poop in their mouth is humorously answered with an equation resulting in 195 years.
Unit cancellation is a strange phenomenon where units used in calculations cancel each other out, resulting in a seemingly nonsensical unit.
Gas mileage is an example of unit cancellation, with US measurements in miles per gallon and European measurements in litres per 100 kilometres leading to a surprising equivalence in square millimetres.
Kilowatt hours are a 'cursed' unit because they result from multiplying power by time, leading to a unit that is difficult to intuitively understand.
Dimensional analysis involves looking at the units in an equation to determine if the equation is correct, which can be useful when working with physical constants.
The Hubble constant, measured in kilometres per second per megaparsec, describes the rate of expansion of the universe.
The Hubble constant can be converted into inverse seconds, and when doing so, it provides a rough approximation of the age of the universe.
The age of the universe is approximately 13.7 billion years, which is surprisingly close to the 14 billion years suggested by the Hubble constant.
Polarisation mode dispersion (PMD) in optical fibres has units of picoseconds per square root kilometre, a result of a random walk model involving different polarisations of light.
The randomness in the manufacturing of optical fibres leads to different polarisations of light moving at different speeds, causing PMD.
The dispersion in optical fibres is measured in picoseconds, with chromatic dispersion building linearly over the length of the fibre.
PMD is different from chromatic dispersion in that it is measured per square root kilometre, reflecting the random walk nature of the fibre's impurities.
The concept of random walks is introduced to explain the units of PMD, where the dispersion increases with the square root of the fibre's length.
The video also discusses the concept of negative and fractional powers in units, which can arise from complex power laws in scientific relationships.
An example of a cursed unit from the speaker's research involves a scattering measure in units of parsecs times meters to the power of minus 20/3.
The speaker's personal experience with cursed units includes a unit of nanometres per square root nanometre from a study on DNA molecules.
The video encourages viewers to share their encounters with cursed units in the comments, highlighting the awkward and inexplicable aspects of the universe.
Transcripts
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