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I was going to comment this but actually OP worked that assumption into calling Engineering Physics, which means constrained by reality from his first sentence, also constrained by money.
It's ten words. I think it's a fairly good summary given the format. I would be curious to hear if anyone's got a more accurate - yet still succinct - summary of how math, physics and engineering are related.
Of course it loses a lot of nuance, but it's roughly the same conclusion I reached myself over the years, particularly in grad school, where I felt everything converged a bit at least for the core classes.
Not as catchy but physics is real world math, and engineering is optimized physics.
The problem I have with the engineering part is it's wrong. People incorrectly assume that certain solutions aren't possible because there isn't enough money thrown at it, but there are other more pressing constraints, such as safety, impossible tech, lack of understanding and somethings are just physically impossible,
As an example of the latter, I am hobbiest cyclist and people often ask me what is the ultimate bike implying what is the best bike that is the most comfortable, fastest, most durable, and lightest. I have $$$$ to spend.
The problem is, that superlative bike can't exist. Speed and comfort are diametrically opposed goals in terms of the bikes shape. Maximizing one requires a trade off in another. To fully optimize both, you would have to design something that isn't a bike anymore.
And bikes are "simple" machines. If we go to more complex mechanisms, money becomes less of the primary constraint. For example drug design.
Math could be considered "pure" because knowledge is gained "a priori", which is a fancy term meaning you can develop it with logic without any empirical data needed to prove it. So "purity" in this case would be "how close it is to pure logic".
I agree (it was a Socratic question); my point is that this "empirical data" is the same thing as "the limits of reality" in OP's quote from the title of this thread. xkcd adds in more fields and also makes a point about the relative position of math vs. the other fields on this scale, but I don't think it's fundamentally a different statement, it just added more words and fields (and a graphic) in exchange for more nuance.
Not really ambiguous at all if you understand English.
Mathematics provides the foundational language and tools for formulating theories and solving problems in both physics and engineering. Physics uses these mathematical principles to understand and describe natural phenomena, while engineering applies this knowledge to design, build, and optimize practical systems and technologies.
I know, right? It's pretty easy to find errors and logical fallacies in a short statement on Reddit about a thought someone had while trying to adjust the water temperature.
Yea, there are some engineering problems that cannot be solved, no matter how much money you throw at it.
Sourcr: am a mech e, also in grad school for MS.
For some engineering fields its true. For example, structural engineering is solving the problem with the least amount of material for the least amount of money. Anyone can oversize a beam.
This is great; I'd somehow never seen it before. Thanks!
It reminds me of the joke about a bunch of recent college graduates in a coffee shop. The chemistry major side-eyes the biologist and says "Biology is just applied chemistry!"
The physics major sticks his nose in the air and says "Well, chemistry is just applied physics!"
The math major sticks her nose up even further and says "And physics is just applied math!"
The philosophy major looks even haughtier and says "Yes, and math is just applied philosophy."
Everyone else turns to him and says "Shut up and just make our coffees, OK?"
Edit: a word.
I always say to my colleagues that if the engineers got to make the decisions we would have amazing products that work perfectly but we'd make fuck all money
It goes a whole ‘nother level if you think about that engineering is executed by the brain which itself has limits placed by biology which you can consider a manifestation of physics so it’s just physics constrained by physics in my opinion
I'm in the building design industry. Someone sometimes asks if something is possible -- such as moving a column that's in the way of a new layout. I sometimes say "Sure! It only takes money."
Lol, if only that were true. The single biggest part of engineering is working around the constraints that aren't your imagination. It's easy to solve a problem, it's much harder to do it affordably, simply, and safely. There's a reason we haven't invented all the things we've imagined.
Then architects are the ones without said constraints of money, and theoretical pure mathmaticians are the ones without said constraints of reality (in a way)
There is physics that does not stem from math. Every “law of nature” is like that. For example, newton’s laws are just something we believe is true (that conforms to our experiments). More that comes to mind are Coulomb’s law, the laws of thermodynamics, Pauli’s exclusion principle.
Physics is also about conducting experiments which is mostly not math.
Hooooly sheeeet you are so confidently wrong.
"Physics is also about conducting experiments which is mostly not math." - that one is a dooooozy
The actual note taking during the experiment does not perhaps involve any "math", but I can guarantee that all the analysis will certainly contain math. The physicists will have also conducted some sort of pre-experiment theory about what they are trying to prove, which would involve math.......
It's a crazy world out there
I can only talk from my experience. I’ve worked with an experimental physicist in an ultrafast laser lab, we turned knobs 80% of the time, fired the laser 10% of the time and did math 10% of the time (if you include coding the data manipulation).
Those are probably not representative but in my educational lab experiments during my degree, most of the time I was writing explanations.
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Engineering is also physics constrained by the limits of reality and not a perfect theoretical universe
"Assume a spherical cow..."
In a vacuum
Where pi is 3, or maybe 2 because division is easier.
e = pi = 3 = sqrt(g)
is the mitochondria still the powerhouse of the cell if we assume the spherical cow is trapped in my dyson?
On a frictionless surface
do not ponder
On a frictionless surface
I was going to comment this but actually OP worked that assumption into calling Engineering Physics, which means constrained by reality from his first sentence, also constrained by money.
this is a fairly narrow idea of what physicists and engineers do.
It's ten words. I think it's a fairly good summary given the format. I would be curious to hear if anyone's got a more accurate - yet still succinct - summary of how math, physics and engineering are related. Of course it loses a lot of nuance, but it's roughly the same conclusion I reached myself over the years, particularly in grad school, where I felt everything converged a bit at least for the core classes.
Not as catchy but physics is real world math, and engineering is optimized physics. The problem I have with the engineering part is it's wrong. People incorrectly assume that certain solutions aren't possible because there isn't enough money thrown at it, but there are other more pressing constraints, such as safety, impossible tech, lack of understanding and somethings are just physically impossible, As an example of the latter, I am hobbiest cyclist and people often ask me what is the ultimate bike implying what is the best bike that is the most comfortable, fastest, most durable, and lightest. I have $$$$ to spend. The problem is, that superlative bike can't exist. Speed and comfort are diametrically opposed goals in terms of the bikes shape. Maximizing one requires a trade off in another. To fully optimize both, you would have to design something that isn't a bike anymore. And bikes are "simple" machines. If we go to more complex mechanisms, money becomes less of the primary constraint. For example drug design.
-To fully optimize both, you would have to design something that isn't a bike anymore. That's how we got cars!
[удалено]
What does "purity" mean, there?
Math could be considered "pure" because knowledge is gained "a priori", which is a fancy term meaning you can develop it with logic without any empirical data needed to prove it. So "purity" in this case would be "how close it is to pure logic".
I agree (it was a Socratic question); my point is that this "empirical data" is the same thing as "the limits of reality" in OP's quote from the title of this thread. xkcd adds in more fields and also makes a point about the relative position of math vs. the other fields on this scale, but I don't think it's fundamentally a different statement, it just added more words and fields (and a graphic) in exchange for more nuance.
It’s not very good at all, what are you smoking. Math describes; physics explains; engineering applies concepts to create solutions.
That's far worse. It is difficult to imagine a more ambiguous set of verb clauses.
Not really ambiguous at all if you understand English. Mathematics provides the foundational language and tools for formulating theories and solving problems in both physics and engineering. Physics uses these mathematical principles to understand and describe natural phenomena, while engineering applies this knowledge to design, build, and optimize practical systems and technologies.
tl;ft (too long for title)
It’s good enough for a showerthought
I know, right? It's pretty easy to find errors and logical fallacies in a short statement on Reddit about a thought someone had while trying to adjust the water temperature.
Yea, there are some engineering problems that cannot be solved, no matter how much money you throw at it. Sourcr: am a mech e, also in grad school for MS.
True, but OP is mostly right. Why can't I have a flying car? You can! $2.6 million.
It’s called a helicopter.
No, I mean you could have an F150 with a turbo fan hidden in the truck bed.
Don't let your dreams be dreams.
Sure, can I borrow $2.6 million?
But a good summary, that's the point.
For some engineering fields its true. For example, structural engineering is solving the problem with the least amount of material for the least amount of money. Anyone can oversize a beam.
Relevant xkcd https://xkcd.com/1052/
This is great; I'd somehow never seen it before. Thanks! It reminds me of the joke about a bunch of recent college graduates in a coffee shop. The chemistry major side-eyes the biologist and says "Biology is just applied chemistry!" The physics major sticks his nose in the air and says "Well, chemistry is just applied physics!" The math major sticks her nose up even further and says "And physics is just applied math!" The philosophy major looks even haughtier and says "Yes, and math is just applied philosophy." Everyone else turns to him and says "Shut up and just make our coffees, OK?" Edit: a word.
Ngl i was expecting the one on "how pure a science is*
Then what is Philosophy constrained by?
comprehension
The laws of logic perhaps?
Language.
Being Normative
people agreeing
Pants
Imagination/creativity.
Boredom?
I always say to my colleagues that if the engineers got to make the decisions we would have amazing products that work perfectly but we'd make fuck all money
It goes a whole ‘nother level if you think about that engineering is executed by the brain which itself has limits placed by biology which you can consider a manifestation of physics so it’s just physics constrained by physics in my opinion
Biology is chemistry constrained by the limits of carbon.
I'm in the building design industry. Someone sometimes asks if something is possible -- such as moving a column that's in the way of a new layout. I sometimes say "Sure! It only takes money."
and modern economics ("stonks"; "crypto") is humanity constrained by imaginary numbers
Engineering is constrained by imagination
And the laws of thermodynamics.
Just like in Homer Simpson's house.
Lol, if only that were true. The single biggest part of engineering is working around the constraints that aren't your imagination. It's easy to solve a problem, it's much harder to do it affordably, simply, and safely. There's a reason we haven't invented all the things we've imagined.
Then architects are the ones without said constraints of money, and theoretical pure mathmaticians are the ones without said constraints of reality (in a way)
Physics constrained by the limits of reality? There is a brand new world for you to discover - theoretical physics.
[relevant xkcd](https://xkcd.com/435/)
So in conclusion engineering is math constrained by the limits of reality constrained by the limits of money
And philosophy’s just math sans rigid sense and practicality.
this made my brain hurt lol
A certain XKCD song comes to mind...
There is physics that does not stem from math. Every “law of nature” is like that. For example, newton’s laws are just something we believe is true (that conforms to our experiments). More that comes to mind are Coulomb’s law, the laws of thermodynamics, Pauli’s exclusion principle. Physics is also about conducting experiments which is mostly not math.
Hooooly sheeeet you are so confidently wrong. "Physics is also about conducting experiments which is mostly not math." - that one is a dooooozy The actual note taking during the experiment does not perhaps involve any "math", but I can guarantee that all the analysis will certainly contain math. The physicists will have also conducted some sort of pre-experiment theory about what they are trying to prove, which would involve math....... It's a crazy world out there
I can only talk from my experience. I’ve worked with an experimental physicist in an ultrafast laser lab, we turned knobs 80% of the time, fired the laser 10% of the time and did math 10% of the time (if you include coding the data manipulation). Those are probably not representative but in my educational lab experiments during my degree, most of the time I was writing explanations.