This is a clip from a conversation with Sean Carroll from Nov 2019. Check out Sean's book on quantum mechanics Something Deeply Hidden. New full episodes once or twice a week and 1-2 new clips or a new non-podcast video on all other days. If you enjoy it, subscribe, comment, and share. You can watch the full conversation here: th-cam.com/video/iNqqOLscOBY/w-d-xo.html (more links below) Podcast full episodes playlist: th-cam.com/play/PLrAXtmErZgOdP_8GztsuKi9nrraNbKKp4.html Podcasts clips playlist: th-cam.com/play/PLrAXtmErZgOeciFP3CBCIEElOJeitOr41.html Podcast website: lexfridman.com/ai Podcast on Apple Podcasts (iTunes): apple.co/2lwqZIr Podcast on Spotify: spoti.fi/2nEwCF8 Podcast RSS: lexfridman.com/category/ai/feed/
I guess, to me, someone who is neither physicist nor mathematician, the difference is that maths can be used to describe all sciences, finance, economics, etc. Whereas physics simply looks at the nature of reality.
I believe either "generalization" or "abstraction" would be a much better word here because that is what math is "doing" in physics. You cannot compress all possible states of a simple pendulum or represent all the paths taken by an electron, on a sheet of paper. Rather, you can generalize these phenomena using mathematical equations and be studied as specific disciplines within math (like chaos theory or probability theory). Information is not compressed by math. It is generalized. And with such generalizations one can gain all the information (may or may not be exact) about a physical system if one has enough computing power.
“As far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality.” - Albert Einstein
I love how physicists are like “well math is useful, but it’s not quite what we do, mathematicians deal in the general case and we actually care about reality.” But the only reason they understand anything is because the general case exists lol thanks to us. Additionally there’s like this attitude of, “well we care about models more than math.” But it’s like well what does a model describe that isn’t mathematical… basically nothing that is tangible. Physics is applied math.
Maths is merely a tool nothing else at least for physics. No one needs general cases at all. General cases exists only because one knows reality. Example, ND is there only because people understood 3D. Overall maths is only a different perspective of what we actually see. Not that important compared to physics chemistry biology, but only an aid. Like a slave of them tbh.
@@0_Nobody Without Riemannian geometry, we cannot rigorously explain general relativity; without functional analysis, we cannot define Hilbert space, which is essential for quantum mechanics. Mathematics is not only a tool for physics; it is a necessity.
Force, energy,mass, quantum fields, space-time continuum,scaler fields and vector fields all are abstract and mathematical concepts. So it kinda hard to dinstiguish physics from mathematics.
In this theory the mathematics of quantum mechanics represents geometry, the Planck Constant ħ=h/2π is linked to 2π circular geometry representing a two dimensional aspect of 4π spherical three-dimensional geometry. We have to square the wave function Ψ² representing the radius being squared r² because the process is relative to the two-dimensional spherical 4π surface. We then see 4π in Heisenberg’s Uncertainty Principle ∆×∆pᵪ≥h/4π representing our probabilistic temporal three dimensions life. The electron e² and the speed of light c² are both squares for the same geometrical reason. This theory explain a Mathematical explanation of creation with the mathematics representing a simple geometrical process! This theory is explained by just one equation (E=ˠM˳C²)∞. With energy ∆E equals mass ∆M linked to the Lorentz contraction ˠ of space and time. The Lorentz contraction ˠ represents the time dilation of Einstein’s Theory of Relativity. We have energy ∆E slowing the rate that time ∆t flows as a universal process of energy exchange or continuous creation. Mass will increase relative to this process with gravity being a secondary force to the electromagnetic force. The c² represents the speed of light c radiating out in a sphere 4π of EMR from its radius forming a square c² of probability. We have to square the probability of the wave-function Ψ because the area of the sphere is equal to the square of the radius of the sphere multiplied by 4π. This simple geometrical process forms the probability and uncertainty of everyday life and at the smallest scale of the process is represented mathematically by Heisenberg’s Uncertainty Principle ∆×∆pᵪ≥h/4π. In such a theory the future is unfolding photon by photon with the movement of charge and flow of EM fields. This gives us a geometrical reason for positive and negative charge with a concaved inner surface for negative charge and a convexed outer surface for positive charge. The brackets in the equation (E=ˠM˳C²)∞ represent a dynamic boundary condition of an individual reference frame with an Arrow of Time or time line for each frame of reference. The infinity ∞ symbol represents an infinite number of dynamic interactive reference frames that are continuously coming in and out of existence. The spontaneous absorption and emission of light is continuously forming a probabilistic future by changing photon ∆E=hf potential energy into the kinetic energy of electrons. Therefore, the electron is squared e² for the same geometrical reason.
Based on E=MC² could a single geometrical process square ψ², t², e², c², v²? We need to go back to r² and the three dimensional physics of the Inverse Square Law. Even back to the spherical 4πr² geometry of Huygens’ Principle of 1670.
Everything representing a consequent equal to itself string of events (like math)/ does not mean its theory represents the best one available in a natural physical world which still allows for it. While it is artificial.
The only reason I avoided the sciences is because of Math. Ohm's law, for instance, looks simple, but the relationship between voltage. current and resistance could be better explained without shoving a formula down someone's throat.
This is a clip from a conversation with Sean Carroll from Nov 2019. Check out Sean's book on quantum mechanics Something Deeply Hidden. New full episodes once or twice a week and 1-2 new clips or a new non-podcast video on all other days. If you enjoy it, subscribe, comment, and share. You can watch the full conversation here: th-cam.com/video/iNqqOLscOBY/w-d-xo.html
(more links below)
Podcast full episodes playlist:
th-cam.com/play/PLrAXtmErZgOdP_8GztsuKi9nrraNbKKp4.html
Podcasts clips playlist:
th-cam.com/play/PLrAXtmErZgOeciFP3CBCIEElOJeitOr41.html
Podcast website:
lexfridman.com/ai
Podcast on Apple Podcasts (iTunes):
apple.co/2lwqZIr
Podcast on Spotify:
spoti.fi/2nEwCF8
Podcast RSS:
lexfridman.com/category/ai/feed/
Sean's first sentence nailed it.
Damn right 👌
Damn true
And yet they hit me with a 30 second ad. F you TH-cam
I guess, to me, someone who is neither physicist nor mathematician, the difference is that maths can be used to describe all sciences, finance, economics, etc. Whereas physics simply looks at the nature of reality.
What about pure math?
@@steliostoulis1875 pure maths is the hardest subject
This man has a great way of connecting what he knows to what is possible which is a gift
Never heard anyone refer to math as compressed information, very interesting.
I think he is referring to theory. Force = mass X acceleration, F=mA, is a very compressed idea but says a lot about the world.
I believe either "generalization" or "abstraction" would be a much better word here because that is what math is "doing" in physics. You cannot compress all possible states of a simple pendulum or represent all the paths taken by an electron, on a sheet of paper. Rather, you can generalize these phenomena using mathematical equations and be studied as specific disciplines within math (like chaos theory or probability theory). Information is not compressed by math. It is generalized. And with such generalizations one can gain all the information (may or may not be exact) about a physical system if one has enough computing power.
@@myothersoul1953 No he is not.
“As far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality.” - Albert Einstein
The problem with maths. Lol
In Physics you cannot divide multiply or subtract from zero. Mathematicians take great delight in doing just that.
I love how physicists are like “well math is useful, but it’s not quite what we do, mathematicians deal in the general case and we actually care about reality.” But the only reason they understand anything is because the general case exists lol thanks to us. Additionally there’s like this attitude of, “well we care about models more than math.” But it’s like well what does a model describe that isn’t mathematical… basically nothing that is tangible. Physics is applied math.
Maths is merely a tool nothing else at least for physics. No one needs general cases at all. General cases exists only because one knows reality. Example, ND is there only because people understood 3D. Overall maths is only a different perspective of what we actually see. Not that important compared to physics chemistry biology, but only an aid. Like a slave of them tbh.
@@0_Nobody Without Riemannian geometry, we cannot rigorously explain general relativity; without functional analysis, we cannot define Hilbert space, which is essential for quantum mechanics. Mathematics is not only a tool for physics; it is a necessity.
Force, energy,mass, quantum fields, space-time continuum,scaler fields and vector fields all are abstract and mathematical concepts. So it kinda hard to dinstiguish physics from mathematics.
In this theory the mathematics of quantum mechanics represents geometry, the Planck Constant ħ=h/2π is linked to 2π circular geometry representing a two dimensional aspect of 4π spherical three-dimensional geometry. We have to square the wave function Ψ² representing the radius being squared r² because the process is relative to the two-dimensional spherical 4π surface. We then see 4π in Heisenberg’s Uncertainty Principle ∆×∆pᵪ≥h/4π representing our probabilistic temporal three dimensions life. The electron e² and the speed of light c² are both squares for the same geometrical reason. This theory explain a Mathematical explanation of creation with the mathematics representing a simple geometrical process! This theory is explained by just one equation (E=ˠM˳C²)∞. With energy ∆E equals mass ∆M linked to the Lorentz contraction ˠ of space and time. The Lorentz contraction ˠ represents the time dilation of Einstein’s Theory of Relativity. We have energy ∆E slowing the rate that time ∆t flows as a universal process of energy exchange or continuous creation. Mass will increase relative to this process with gravity being a secondary force to the electromagnetic force. The c² represents the speed of light c radiating out in a sphere 4π of EMR from its radius forming a square c² of probability. We have to square the probability of the wave-function Ψ because the area of the sphere is equal to the square of the radius of the sphere multiplied by 4π. This simple geometrical process forms the probability and uncertainty of everyday life and at the smallest scale of the process is represented mathematically by Heisenberg’s Uncertainty Principle ∆×∆pᵪ≥h/4π. In such a theory the future is unfolding photon by photon with the movement of charge and flow of EM fields. This gives us a geometrical reason for positive and negative charge with a concaved inner surface for negative charge and a convexed outer surface for positive charge. The brackets in the equation (E=ˠM˳C²)∞ represent a dynamic boundary condition of an individual reference frame with an Arrow of Time or time line for each frame of reference. The infinity ∞ symbol represents an infinite number of dynamic interactive reference frames that are continuously coming in and out of existence. The spontaneous absorption and emission of light is continuously forming a probabilistic future by changing photon ∆E=hf potential energy into the kinetic energy of electrons. Therefore, the electron is squared e² for the same geometrical reason.
Based on E=MC² could a single geometrical process square ψ², t², e², c², v²?
We need to go back to r² and the three dimensional physics of the Inverse Square Law. Even back to the spherical 4πr² geometry of Huygens’ Principle of 1670.
Good point
Love me some GANs. Math is the tool they use for discovery and yet they sh!t on the actual tool itself that gets them popularity.
Everything representing a consequent equal to itself string of events (like math)/ does not mean its theory represents the best one available in a natural physical world which still allows for it. While it is artificial.
Schroder's cat solution...put him in a glass box. Transparency leads to truth, truth sets you free .Dead or alive.
All possible worlds? So, who invented the axioms?
Close your eyes. Dr. Howard Stern, everyone.
I was listening until Mr Carroll mentioned multiverses…
There exists no such thing as "wrong math". Recant now upon threat of severe penalties.
Thx
Love it !
The only reason I avoided the sciences is because of Math. Ohm's law, for instance, looks simple, but the relationship between voltage. current and resistance could be better explained without shoving a formula down someone's throat.
Physics is physics but Math is Mathematics.
Mathematics is the Language of Physics,Sir.
Maths is the language of the universe
Czypu not really- it’s a language we have developed to describe our perceptions
Czypu and to describe our conceptions
@@crypastesomemore8348 but so far it worked to everything we applied it to, you can predict the universe through equations
@@crypastesomemore8348 nope, where our perceptiona fail, we have math, sometimes could be very counter intuitive like in quantum mechanics