5 ms·

Non-Euclidean geometry (geometric axioms in which one postulate is rejected such that the 3 angles of a triangle are not exactly 180 degrees) was considered a m

Non-Euclidean geometry (geometric axioms in which one postulate is rejected such that the 3 angles of a triangle are not exactly 180 degrees) was considered a meaningless word game and fundamental mistruth. Later, non-Euclidean geometry was actually essential to modern physics. It's intellectually sketchy to judge future value by the present.

cess11 9mo ago
I imagine that elliptic geometry had some use before modern physics.
- saghm 9mo ago
  Yeah, even just trying chart a course on a ship across a reasonable distance will cause you to need to reevaluate some "obvious" things (like "what path is the shortest between these two ports" being a curve rather than a line).
- ecosystem 9mo ago
  The specific controversy was whether without the parallel/5th postulate, there existed a logical contradiction, i.e. proving the parallel postulate
emil-lp 9mo ago
In the 1700s, perhaps. But we have come a long way since that.
- ecosystem 9mo ago
  Yet, OP is repeating the same logical fallacy: the absence of a result is not a result of absence.
PunchyHamster 9mo ago
Might as well fund someone researching whether quantum theory run on little gnomes, if there is no serious path to verification after 50 years, why not quantum gnomes?
- Elextric 9mo ago
  Ideally, one should explore all possibilities. It is remarkable how far "merely" predicting the next word has taken us.
  - PunchyHamster 9mo ago
    That was constant progress with measurable goals, not "big things are coming decade from now" every decade.
- Tadpole9181 9mo ago
  > We should stop funding research into prime numbers. They're stupid and useless. Who cares about them, if they will never be used for anything? Number theory should be stopped, you may as well research gnomes. I imagine this is what you would have sounded like 100 years ago.
  - dgfl 9mo ago
    You may be understating how much 15 orders of magnitude are. The only truly exponential technological progress we’ve ever had, transistors, only scaled by ~5 orders of magnitude in feature size. Thermal engines went from maybe 0.1% to ~50%, less than 3 orders of magnitude, in about 200 years. There’s very fundamental physical laws that suggest that engines are done, and transistor scaling as we have known it for 30 years is also done. Perhaps very clever things might give us 5 more orders of magnitude? E.g. truly 3D integration somehow? Then we’re still 5 orders of magnitude off from our target. I can’t think of any technology that ever improved by more than 10^6, perhaps 10^9 if you count some derivative number (like “number of transistors on chip”, rather than actual size), and that’s from literally zero to today. Not from already-pretty-advanced to Death Star scale. Another perspective is that, to get to those kinetic energies, we need accelerators as large as the solar system. Possibly the galaxy, I can’t quite remember. Will you concede that galaxy-wide objects are so far from current reality that there’s no point seriously talking about them?
    - Tadpole9181 9mo ago
snapplebobapple 9mo ago
you are mixing up gambling spend vs whole industry spend. If string theory was a small handful of people making up a small m*nority of physics departments like non-euclidea geometry research was that would be fine. Its huge swaths of most physics departments and a huge suck on research funding. For that kind of spend you better show results because you are in production phase at that point not lotto ticket moonshit phase. If we are buying lotto tickets with the money bey lots of different lotto tickets not a whole bunch of one lotto ticket
- Tadpole9181 9mo ago
  I think you are vastly overestimating the number of string physicists and how much their non-experimental research costs. There's maybe a couple or few hundred-ish in the whole world that focus on it. And they don't need much money because it's pretty much all math.
  - boznz 9mo ago
    As a percentage of theoretical physicists it is probably significant though. A Better question is how much love/money/attention is going into rival theories ?
    - snapplebobapple 9mo ago
      It is basically this. People arguing for string theory have no concept of how to maximize return with uncertainty. The thing had 50 years of substantial funding and substantial mindshare and pushed us nowhere. Any rational person with basic risk understanding would know at this point its a fail and we are in the not knowing what to pursue phase so we should be supporting small investments in dicerse options &ntil something promising happens then we can concentrate funding there &ntil that times out or gices us the understanding to achieve something new and great. The lifecycle of increasingly aupporting string theory s=ould have turned 2 to 3 decades ago instead of just recently. We lost atleast 20 and more like 30 years of progress we didnt have because a bunch of very smart people captured the physics funding aparatus to enrich thselves.
- 9mo ago
constantcrying 9mo ago
>Non-Euclidean geometry (geometric axioms in which one postulate is rejected such that the 3 angles of a triangle are not exactly 180 degrees) was considered a meaningless word game and fundamental mistruth. This is just a lie though. Non-Euclidean geometry is a mathematical model of how distances behave on non-linear spaces. Nobody ever believed it to be a "fundamental mistruth", even suggesting it would look ridiculous. It would be akin to denying linear algebra, even the meaning is unclear. That the physical reality of space is not linear was a shocking revelation, since all human experience and basically every experiment done up until that point indicated otherwise.
- ecosystem 9mo ago
  This is a generally known part of the history of mathematics. > Nobody ever believed it to be a "fundamental mistruth" https://math.libretexts.org/Courses/College_of_the_Canyons/Math_100:_Liberal_Arts_Mathematics_(Saburo_Matsumoto)/09:_Selected_Topics/9.05:_Non-Euclidean_Geometry https://math.libretexts.org/Courses/College_of_the_Canyons/M... "Lobachevsky [mathematician contemporary of Gauss, who claimed parallel postulate was unnecessary] was relentlessly criticized, mocked, and rejected by the academic world. His new “imaginary” geometry represented the “shamelessness of false new inventions”" Further, many claimed premature success in finding logical contridictions in geometry lacking parallel (Euclid's 5th) postulate; which meant they believed a 4-postulate geometry to be fundamentally false.

cess11 9mo ago

I imagine that elliptic geometry had some use before modern physics.

saghm 9mo ago
Yeah, even just trying chart a course on a ship across a reasonable distance will cause you to need to reevaluate some "obvious" things (like "what path is the shortest between these two ports" being a curve rather than a line).
ecosystem 9mo ago
The specific controversy was whether without the parallel/5th postulate, there existed a logical contradiction, i.e. proving the parallel postulate

emil-lp 9mo ago

In the 1700s, perhaps. But we have come a long way since that.

ecosystem 9mo ago
Yet, OP is repeating the same logical fallacy: the absence of a result is not a result of absence.

PunchyHamster 9mo ago

Might as well fund someone researching whether quantum theory run on little gnomes, if there is no serious path to verification after 50 years, why not quantum gnomes?

Elextric 9mo ago
Ideally, one should explore all possibilities. It is remarkable how far "merely" predicting the next word has taken us.
- PunchyHamster 9mo ago
  That was constant progress with measurable goals, not "big things are coming decade from now" every decade.
Tadpole9181 9mo ago
> We should stop funding research into prime numbers. They're stupid and useless. Who cares about them, if they will never be used for anything? Number theory should be stopped, you may as well research gnomes. I imagine this is what you would have sounded like 100 years ago.
- dgfl 9mo ago
  You may be understating how much 15 orders of magnitude are. The only truly exponential technological progress we’ve ever had, transistors, only scaled by ~5 orders of magnitude in feature size. Thermal engines went from maybe 0.1% to ~50%, less than 3 orders of magnitude, in about 200 years. There’s very fundamental physical laws that suggest that engines are done, and transistor scaling as we have known it for 30 years is also done. Perhaps very clever things might give us 5 more orders of magnitude? E.g. truly 3D integration somehow? Then we’re still 5 orders of magnitude off from our target. I can’t think of any technology that ever improved by more than 10^6, perhaps 10^9 if you count some derivative number (like “number of transistors on chip”, rather than actual size), and that’s from literally zero to today. Not from already-pretty-advanced to Death Star scale. Another perspective is that, to get to those kinetic energies, we need accelerators as large as the solar system. Possibly the galaxy, I can’t quite remember. Will you concede that galaxy-wide objects are so far from current reality that there’s no point seriously talking about them?
  - Tadpole9181 9mo ago

snapplebobapple 9mo ago

you are mixing up gambling spend vs whole industry spend. If string theory was a small handful of people making up a small m*nority of physics departments like non-euclidea geometry research was that would be fine. Its huge swaths of most physics departments and a huge suck on research funding. For that kind of spend you better show results because you are in production phase at that point not lotto ticket moonshit phase. If we are buying lotto tickets with the money bey lots of different lotto tickets not a whole bunch of one lotto ticket

Tadpole9181 9mo ago
I think you are vastly overestimating the number of string physicists and how much their non-experimental research costs. There's maybe a couple or few hundred-ish in the whole world that focus on it. And they don't need much money because it's pretty much all math.
- boznz 9mo ago
  As a percentage of theoretical physicists it is probably significant though. A Better question is how much love/money/attention is going into rival theories ?
  - snapplebobapple 9mo ago
    It is basically this. People arguing for string theory have no concept of how to maximize return with uncertainty. The thing had 50 years of substantial funding and substantial mindshare and pushed us nowhere. Any rational person with basic risk understanding would know at this point its a fail and we are in the not knowing what to pursue phase so we should be supporting small investments in dicerse options &ntil something promising happens then we can concentrate funding there &ntil that times out or gices us the understanding to achieve something new and great. The lifecycle of increasingly aupporting string theory s=ould have turned 2 to 3 decades ago instead of just recently. We lost atleast 20 and more like 30 years of progress we didnt have because a bunch of very smart people captured the physics funding aparatus to enrich thselves.
9mo ago

constantcrying 9mo ago

>Non-Euclidean geometry (geometric axioms in which one postulate is rejected such that the 3 angles of a triangle are not exactly 180 degrees) was considered a meaningless word game and fundamental mistruth. This is just a lie though. Non-Euclidean geometry is a mathematical model of how distances behave on non-linear spaces. Nobody ever believed it to be a "fundamental mistruth", even suggesting it would look ridiculous. It would be akin to denying linear algebra, even the meaning is unclear. That the physical reality of space is not linear was a shocking revelation, since all human experience and basically every experiment done up until that point indicated otherwise.

ecosystem 9mo ago
This is a generally known part of the history of mathematics. > Nobody ever believed it to be a "fundamental mistruth" https://math.libretexts.org/Courses/College_of_the_Canyons/Math_100:_Liberal_Arts_Mathematics_(Saburo_Matsumoto)/09:_Selected_Topics/9.05:_Non-Euclidean_Geometry https://math.libretexts.org/Courses/College_of_the_Canyons/M... "Lobachevsky [mathematician contemporary of Gauss, who claimed parallel postulate was unnecessary] was relentlessly criticized, mocked, and rejected by the academic world. His new “imaginary” geometry represented the “shamelessness of false new inventions”" Further, many claimed premature success in finding logical contridictions in geometry lacking parallel (Euclid's 5th) postulate; which meant they believed a 4-postulate geometry to be fundamentally false.