Yep, no doubt there are definitely issues with inflation. My main point is that the size of black holes in the early universe is largely orthogonal to the whole big bang/inflation debate. Even if the model changes, the…
The evidence for the big bang is generally not that if you look far enough back in a telescope, the universe looks younger, which is somewhat the layperson's confusion. Evidence for the big bang is about measuring…
Here's how to appreciate it in terms of the counterfactual: Suppose kinetic energy was E = m|v| instead, linearly dependent on speed |v|. What does that mean for the universe? The traditional Lagrangian is L = 1/2 mv^2…
NPM only gained minimum package age in February of this year, and still doesn't support package exclusions for internal packages. https://github.com/npm/cli/pull/8965 https://github.com/npm/cli/issues/8994 Its good that…
Willingness to look stupid and intellectual self-confidence are two sides of the same coin. If you can find internal (rather than external) reasons to trust/believe in your own intelligence and capabilities, it makes it…
You need to differentiate between special and general relativity when making these statements. It is absolutely true that someone else would have come up with special relativity very soon after Einstein. All that would…
> If, then, it is true that the axiomatic basis of theoretical physics cannot be extracted from experience but must be freely invented, can we ever hope to find the right way? Nay, more, has this right way any existence…
Peter Woit, the Columbia maths department computer systems administrator, makes his bread by googling the word String Theory and then posting what ever latest results come up in a disingenuous way on his blog to stir…
Something the computer scientists of Hackernews might not realise is that most mathematicians are by nature Platonists, even if they would not try to defend that position when pressed. most mathematicians act as though…
https://youtu.be/EbzESiemPHs?si=4UNA7JGPt7OmfnOi&t=206 Here's Gromov, one of the greatest geometers of the last 50 years, discussing his viewpoint on this.
Simons himself completely disspells this idea in his interview on Numberphile.
The EMH is a description of how the market behaves when a sufficiently large number of independent actors are looking for alpha. It is not a prescription of how the market should behave. The conclusion is that with a…
The practical experience of doing mathematics is actually quite close to a natural science, even if the subject is technically a "formal science* according to the conventional meanings of the terms. Mathematicians…
>Today, mathematics is regarded as an abstract science. Pure mathematics is regarded as an abstract science, which it is by definition. Arnol'd argued vehemently and much more convincingly for the viewpoint that all…
This is related to Terence Tao's notion of the stages of mathematical rigor. As Tao puts it, the value of intuition becomes much higher in the post-rigorous stage once you have sufficiently developed your technical…
I certainly am not making any comments about her experiences for sure! Academia is difficult and full of terrible stories, and its not surprising that it causes many people to become exceedingly bitter and contrarian…
As an expert in at least some of the things Sabine makes videos about (string theory), Sabine is a contrarian who, if you are not otherwise an expert on what she is talking about, it would be best to avoid. Sabine, like…
Wildberger is a crank
A theorem which is true in every model is provable by Godel's completeness theorem. Since this theorem is true for the standard model of the natural numbers but not provable, it follows there are nonstandard models of…
The actual answer is the assumptions which define a self-propagating wave do not apply once the wave leaves a vacuum. When it becomes incident onto some medium, due to the coupling of electrons within the medium to the…
One of two things: Either what we know about black hole formation is basically complete (it goes gas -> star -> black hole -> accretion + collisions) but the environment in the early universe was sufficiently…
Also important to note that the process of stellar collapse and then black hole accretion takes absolutely enormous amounts of time to collate a large amount of mass together. It's also an extremely energetic process,…
On that of course I agree, but mathematicians tend to "relegate" such things to exercises. This tends to look pretty bad to enthusiasts reading books because the key examples aren't explored in detail in the main text…
> I’m sure it’s important if you want to be a mathematician, but if you just want to understand enough to be able to use it? This book is for people who want to be mathematicians.
Mathematicians are well aware of complaints like these about introductions to their subjects, by the way. It is for a reason that this book introduces the theory of abstract vector spaces and linear transformations,…
Yep, no doubt there are definitely issues with inflation. My main point is that the size of black holes in the early universe is largely orthogonal to the whole big bang/inflation debate. Even if the model changes, the…
The evidence for the big bang is generally not that if you look far enough back in a telescope, the universe looks younger, which is somewhat the layperson's confusion. Evidence for the big bang is about measuring…
Here's how to appreciate it in terms of the counterfactual: Suppose kinetic energy was E = m|v| instead, linearly dependent on speed |v|. What does that mean for the universe? The traditional Lagrangian is L = 1/2 mv^2…
NPM only gained minimum package age in February of this year, and still doesn't support package exclusions for internal packages. https://github.com/npm/cli/pull/8965 https://github.com/npm/cli/issues/8994 Its good that…
Willingness to look stupid and intellectual self-confidence are two sides of the same coin. If you can find internal (rather than external) reasons to trust/believe in your own intelligence and capabilities, it makes it…
You need to differentiate between special and general relativity when making these statements. It is absolutely true that someone else would have come up with special relativity very soon after Einstein. All that would…
> If, then, it is true that the axiomatic basis of theoretical physics cannot be extracted from experience but must be freely invented, can we ever hope to find the right way? Nay, more, has this right way any existence…
Peter Woit, the Columbia maths department computer systems administrator, makes his bread by googling the word String Theory and then posting what ever latest results come up in a disingenuous way on his blog to stir…
Something the computer scientists of Hackernews might not realise is that most mathematicians are by nature Platonists, even if they would not try to defend that position when pressed. most mathematicians act as though…
https://youtu.be/EbzESiemPHs?si=4UNA7JGPt7OmfnOi&t=206 Here's Gromov, one of the greatest geometers of the last 50 years, discussing his viewpoint on this.
Simons himself completely disspells this idea in his interview on Numberphile.
The EMH is a description of how the market behaves when a sufficiently large number of independent actors are looking for alpha. It is not a prescription of how the market should behave. The conclusion is that with a…
The practical experience of doing mathematics is actually quite close to a natural science, even if the subject is technically a "formal science* according to the conventional meanings of the terms. Mathematicians…
>Today, mathematics is regarded as an abstract science. Pure mathematics is regarded as an abstract science, which it is by definition. Arnol'd argued vehemently and much more convincingly for the viewpoint that all…
This is related to Terence Tao's notion of the stages of mathematical rigor. As Tao puts it, the value of intuition becomes much higher in the post-rigorous stage once you have sufficiently developed your technical…
I certainly am not making any comments about her experiences for sure! Academia is difficult and full of terrible stories, and its not surprising that it causes many people to become exceedingly bitter and contrarian…
As an expert in at least some of the things Sabine makes videos about (string theory), Sabine is a contrarian who, if you are not otherwise an expert on what she is talking about, it would be best to avoid. Sabine, like…
Wildberger is a crank
A theorem which is true in every model is provable by Godel's completeness theorem. Since this theorem is true for the standard model of the natural numbers but not provable, it follows there are nonstandard models of…
The actual answer is the assumptions which define a self-propagating wave do not apply once the wave leaves a vacuum. When it becomes incident onto some medium, due to the coupling of electrons within the medium to the…
One of two things: Either what we know about black hole formation is basically complete (it goes gas -> star -> black hole -> accretion + collisions) but the environment in the early universe was sufficiently…
Also important to note that the process of stellar collapse and then black hole accretion takes absolutely enormous amounts of time to collate a large amount of mass together. It's also an extremely energetic process,…
On that of course I agree, but mathematicians tend to "relegate" such things to exercises. This tends to look pretty bad to enthusiasts reading books because the key examples aren't explored in detail in the main text…
> I’m sure it’s important if you want to be a mathematician, but if you just want to understand enough to be able to use it? This book is for people who want to be mathematicians.
Mathematicians are well aware of complaints like these about introductions to their subjects, by the way. It is for a reason that this book introduces the theory of abstract vector spaces and linear transformations,…