There is a name for the sum over "God Equation". It is called the partition function. Here is a description of the partition function from David Tong, a professor at Cambridge University, in his book Statistical Field Theory: "Even though Z (partition function) is first introduced as an innocuous normalisation factor, it actually contains everything we want to know about the system." Here is a wiki page on the partition function: en.wikipedia.org/wiki/Partition_function_(mathematics)
@@CompuFlair The partition function is not typically referred to as the "God equation." The term "God equation" isn't a formal concept in physics or machine learning. If someone used the term "God equation" for the partition function, it would likely be in a metaphorical or philosophical sense, reflecting its central role in understanding a wide range of physical systems through statistical mechanics. However, it is not a commonly accepted term.
I think it is very important to be careful about what we call "probability". The example that you mention, it is not the probability because the probability is zero for measure zero sets. A range of number with non zero measure would have probabilities.
Great work and I absolutely love where you are headed. I have a friendly comment tho. I think it would be more beneficial to clearly point out the usual terms used in this field rather than resorting to hype with terms such as god equation. The machine learning enthusiast would be more informed if you point out related ideas such as SoftMax, Boltzmann distribution, energy-based models and so on.
Mmh, i'm a physicist too, however I don't think that what machine learning does can always be related to the probability distribution with a partition function cause many thing in nature are path dependent or non-Markovian and ML is able to capture path dependencies, statistical mechanics do not.
Thanks for the comment. In its exact form you are probably right. We can't turn 100% of machine learning into partition function in their exact forms. But, I wouldn't underestimate the power of perturbation theory and effective field theories.
I was skeptical, but I plugged in the correct numbers, and, indeed, I stopped the war in Israel, the war in Ukraine, and fed and housed all the poor of this world! Thanks, for sharing the "God Equation." Without it, the world would be hell.
thanks for the comment, the sum over P is the partition function. While in physics the starting point is most of the time the partition function, in machine learning the starting point is probability.
does this god equation have a name?
There is a name for the sum over "God Equation". It is called the partition function.
Here is a description of the partition function from David Tong, a professor at Cambridge University, in his book Statistical Field Theory:
"Even though Z (partition function) is first introduced as an innocuous normalisation factor, it actually contains everything we want to know about the system."
Here is a wiki page on the partition function:
en.wikipedia.org/wiki/Partition_function_(mathematics)
@@CompuFlair The partition function is not typically referred to as the "God equation." The term "God equation" isn't a formal concept in physics or machine learning. If someone used the term "God equation" for the partition function, it would likely be in a metaphorical or philosophical sense, reflecting its central role in understanding a wide range of physical systems through statistical mechanics. However, it is not a commonly accepted term.
The partition function is pretty darn important in Thermodynamics and Statistical Mechanics
That is right, it has all the info about the system, hence the name
I think it is very important to be careful about what we call "probability". The example that you mention, it is not the probability because the probability is zero for measure zero sets. A range of number with non zero measure would have probabilities.
Great work and I absolutely love where you are headed. I have a friendly comment tho. I think it would be more beneficial to clearly point out the usual terms used in this field rather than resorting to hype with terms such as god equation. The machine learning enthusiast would be more informed if you point out related ideas such as SoftMax, Boltzmann distribution, energy-based models and so on.
Thanks for the comment and the tips!
Thank you so much
You are welcome!
Great! You are great! and you have a super well way to explain! Thanks!...
Im glad you liked it!
Mmh, i'm a physicist too, however I don't think that what machine learning does can always be related to the probability distribution with a partition function cause many thing in nature are path dependent or non-Markovian and ML is able to capture path dependencies, statistical mechanics do not.
Thanks for the comment. In its exact form you are probably right. We can't turn 100% of machine learning into partition function in their exact forms. But, I wouldn't underestimate the power of perturbation theory and effective field theories.
I was skeptical, but I plugged in the correct numbers, and, indeed, I stopped the war in Israel, the war in Ukraine, and fed and housed all the poor of this world! Thanks, for sharing the "God Equation." Without it, the world would be hell.
Nice explanation. Like the way you described this. But you should have put the link to the next video in the information or at the end of the video :)
Thanks for the comment. I'll do it next time :)
Isnt this just the partition function? Why not show it in summation notation? Also good video!
thanks for the comment, the sum over P is the partition function. While in physics the starting point is most of the time the partition function, in machine learning the starting point is probability.
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I got confused at @5:20
Which part is confusing?