4 ms·

As much as I enjoy Asimov, I have to say that he is wrong. The gap between what we know and what is true might have decreased immensely, but it is still infinit

by fnovd 3y ago

As much as I enjoy Asimov, I have to say that he is wrong. The gap between what we know and what is true might have decreased immensely, but it is still infinite. Any quantifiable increase is 0 in relation to infinity. Asimov's counter-argument that we are quantifiably less wrong than we were in the past simply does not overcome this core issue. If there is an infinite amount of knowledge separating what we know from what is true, then we can learn an infinite amount of things and still have an infinite amount of things left to learn. To feel justified in thinking the universe is "essentially" understood is to be OK with one's concept of the "essential nature" of the universe to be inherently divergent from a future concept, which according to Asimov's own argument is going to be more correct than our own. To me, it reads as a bitterness towards mortality, a sort of sour grapes: the insights we will have about the universe at some future time must not be very interesting compared to what we know now, because I won't be around to know them. edit: I guess I shouldn't be surprised that Asimov's perspective is shared here. It's very easy to understand the essential nature of the universe when you define the universe as the parts you understand. I don't think human beings in 1000 years will look at our current understanding as special in any way. As transformative as our era is, it will be dwarfed by the scale of transformation in future eras. It's just the most transformative era so far. That's temporal bias, nothing more.

cnity 3y ago
One way to see Asimov's "infinity of wrongness" is perhaps as a fractal. You could view the bulbs in the mandelbrot as being a kind of knowledge, and the "main bulb" occupying the majority of the area belonging to the set as the set of truths known about our universe. The mandelbrot set is infinite in complexity, however its area is finite and bounded! Or as ironing out the wrinkles on a great big t-shirt, where each wrinkle is sub-wrinkled with smaller wrinkles and so on. We've "ironed out" the biggest wrinkles, there are infinitely more but they are much smaller. We're perhaps over half-way ironed, in a quantitative sense.
- fnovd 3y ago
  I disagree fundamentally. You may as well ask me to imagine Earth as a disc, with multiple rotating spotlights shining down on it and a giant ice wall around the edges. I understand what the image is trying to convey, I simply do not agree that this is the shape of the thing I experience.
nathan_compton 3y ago
One might plausibly assert that while the particulars of the universe may be infinite, the fundamental rules which govern the universe are finite and thus at least in principle entirely knowable. While I don't think the 20th century makes an air tight case for the latter, I think it isn't an unreasonable conclusion to draw from 20th Century Physics either.
- ndsipa_pomu 3y ago
  It's surprising that we find ourselves in a universe which does appear to obey certain laws. There's a whole bunch of assumptions made to help us understand how things work and it turns out they're mostly correct. i.e. It's more astounding that we CAN understand the universe and how well maths can act as a model/language to understand it.
  - nathan_compton 3y ago
    Not that surprising. A universe without predictable laws would be unlikely to host life. I mean physics really only knows how to do statics and oscillations and those things work because many systems are at equilibrium or just slightly perturbed from it, probably because of the mysterious low entropy condition which defines the past.
jgeada 3y ago
I think you missed the entire point of the essay. You should actually read it. Science is incremental, revolutions in science mostly just adjust the edges of our knowledge, at more and more extreme corner cases (extreme high energies, extreme high/low temperatures, etc). No, we absolutely don't know it all, but as always, new knowledge and theories will only affect those edges, and refine the predictions for the nth+1 decimal place. By and by, the science that directly affects our daily lives has remained stable and most progress has been in the engineering to put all this knowledge to practical and efficient use.
- mistermann 3y ago
  I like how in English one can make it appear if one is skilfully and logically dismissing an argument without actually even trying to. I don't presume that this was your intent, but the phenomenon is quite interesting and I quite confidently believe dangerous (in that it contributes to some degree to inaccurate models in the minds of those who ingest such text, and those models are what drive action, much of which is harmful...which is easy to see in {choose your outgroup}, but far less easy to see in one's ingroup).
kubanczyk 3y ago
> The gap between what we know and what is true might have decreased immensely, but it is still infinite. The other two commenters have taken different approaches to infinity, but it seems that your argument doesn't hold even for a plain-as-in-real-numbers infinity. Being satisfied with finite knowledge gains, I have no hope to achieve 1% of infinity (or any other fraction of infinity). The universe is infinite in size, another assumption. If I'd fly on vacation to Tenerife, a quantifiable shift of my position by mere thousands of miles would be "zero in relation to infinity". Yet, it's not unimportant for my rest. Talking about infinity doesn't automatically cancel all the finite measurements and bring them to zero.
glitchc 3y ago
Well, we can start by asserting that we do not know everything. We can assert this from the contra positive: If we did know everything, then we would have an acceptable solution to all of our problems. Since we do not, it stands to reason that we don't know everything. Once we accept that the assertion is valid, then it raises the likelihood that our understanding of the world is incomplete in some way. And furthermore is incomplete to different degrees along multiple dimensions of knowledge. Whether incomplete or wrong is a word choice, it doesn't change what's missing. So with each new discovery, our understanding improves, our wrongness decreases.
- cnity 3y ago
  > If we did know everything, then we would have an acceptable solution to all of our problems. Since we do not, it stands to reason that we don't know everything. This can be proven false by contradiction: it may be possible to _know_ that one of our problems has no solution.
  - glitchc 3y ago
    > This can be proven false by contradiction: it may be possible to _know_ that one of our problems has no solution. This claim requires a bit more explanation, not sure if possible. Can you elaborate, or use an example?
ndsipa_pomu 3y ago
I think your use of infinity isn't particularly helpful here as it leads to the contradiction that knowing more doesn't lessen the knowledge gap, whereas it does appear to do so. Maybe, a better interpretation would be that as we learn and understand more, we approach the limits of knowledge. Now it may take an infinite amount of knowledge to actually reach the limits of knowledge (c.f. an infinite series can approach a finite value, but takes forever to get there), but it can still be shown that we are getting nearer. The other aspect is that as we understand more, we appreciate that there's even more to understand, but that can be thought of as our precision increasing and looking at the available knowledge in greater detail.
- fnovd 3y ago
  There is no contradiction because there is no limit of knowledge. The limit of y = e^x is infinity. You can keep increasing x and y will increase exponentially. So you plot the function, let's say with the x axis going up to 10 and the y axis going up to e^10. The graph shows very clearly that, while there was progress before, we have even more progress now. Exponentially more, even! What came before is dwarfed by what we have now; if you look at the range of y for x values 9-10 you can see how little of a difference all those others values (1-8) had between one another, compared to the changes we have now. The rate of change is so high that we're basically in an era of semi-complete knowledge. We must be at some kind of inflection point, this is truly a unique era of understanding. Then you repeat. Set the x axis to 100, and the y axis up to e^100. Oh wait, it's the same graph. That's because it's always the same graph. It's scale-invariant. The slope at every point is always whatever y is. We're always at right at the limit of explaining the "essential nature" of the universe because the "essential nature" of the universe can only be (to us) what we can understand it to be. We chose e^10 as the limit of the y-axis in our first exercise because that's all the knowledge we knew about. We chose e^100 as the limit of the y-axis in our second exercise because that, too, was all the knowledge we knew about. Choosing these random values as the limits of our function (i.e. the limit of the "essential nature of the universe") leaks information into the visualization that will always paint a picture showing that we're at the most transformative time there ever was. When we do it that way, we will always come to the same _wrong_ conclusion. We will always dwarf what came before and be dwarfed by what comes after. To think that we're actually living in an inflection point is hubris, it's wishful thinking, it's the sour grapes of mortality.

by fnovd 3y ago

cnity 3y ago

One way to see Asimov's "infinity of wrongness" is perhaps as a fractal. You could view the bulbs in the mandelbrot as being a kind of knowledge, and the "main bulb" occupying the majority of the area belonging to the set as the set of truths known about our universe. The mandelbrot set is infinite in complexity, however its area is finite and bounded! Or as ironing out the wrinkles on a great big t-shirt, where each wrinkle is sub-wrinkled with smaller wrinkles and so on. We've "ironed out" the biggest wrinkles, there are infinitely more but they are much smaller. We're perhaps over half-way ironed, in a quantitative sense.

fnovd 3y ago
I disagree fundamentally. You may as well ask me to imagine Earth as a disc, with multiple rotating spotlights shining down on it and a giant ice wall around the edges. I understand what the image is trying to convey, I simply do not agree that this is the shape of the thing I experience.

nathan_compton 3y ago

One might plausibly assert that while the particulars of the universe may be infinite, the fundamental rules which govern the universe are finite and thus at least in principle entirely knowable. While I don't think the 20th century makes an air tight case for the latter, I think it isn't an unreasonable conclusion to draw from 20th Century Physics either.

ndsipa_pomu 3y ago
It's surprising that we find ourselves in a universe which does appear to obey certain laws. There's a whole bunch of assumptions made to help us understand how things work and it turns out they're mostly correct. i.e. It's more astounding that we CAN understand the universe and how well maths can act as a model/language to understand it.
- nathan_compton 3y ago
  Not that surprising. A universe without predictable laws would be unlikely to host life. I mean physics really only knows how to do statics and oscillations and those things work because many systems are at equilibrium or just slightly perturbed from it, probably because of the mysterious low entropy condition which defines the past.

jgeada 3y ago

I think you missed the entire point of the essay. You should actually read it. Science is incremental, revolutions in science mostly just adjust the edges of our knowledge, at more and more extreme corner cases (extreme high energies, extreme high/low temperatures, etc). No, we absolutely don't know it all, but as always, new knowledge and theories will only affect those edges, and refine the predictions for the nth+1 decimal place. By and by, the science that directly affects our daily lives has remained stable and most progress has been in the engineering to put all this knowledge to practical and efficient use.

mistermann 3y ago
I like how in English one can make it appear if one is skilfully and logically dismissing an argument without actually even trying to. I don't presume that this was your intent, but the phenomenon is quite interesting and I quite confidently believe dangerous (in that it contributes to some degree to inaccurate models in the minds of those who ingest such text, and those models are what drive action, much of which is harmful...which is easy to see in {choose your outgroup}, but far less easy to see in one's ingroup).

kubanczyk 3y ago

> The gap between what we know and what is true might have decreased immensely, but it is still infinite. The other two commenters have taken different approaches to infinity, but it seems that your argument doesn't hold even for a plain-as-in-real-numbers infinity. Being satisfied with finite knowledge gains, I have no hope to achieve 1% of infinity (or any other fraction of infinity). The universe is infinite in size, another assumption. If I'd fly on vacation to Tenerife, a quantifiable shift of my position by mere thousands of miles would be "zero in relation to infinity". Yet, it's not unimportant for my rest. Talking about infinity doesn't automatically cancel all the finite measurements and bring them to zero.

glitchc 3y ago

Well, we can start by asserting that we do not know everything. We can assert this from the contra positive: If we did know everything, then we would have an acceptable solution to all of our problems. Since we do not, it stands to reason that we don't know everything. Once we accept that the assertion is valid, then it raises the likelihood that our understanding of the world is incomplete in some way. And furthermore is incomplete to different degrees along multiple dimensions of knowledge. Whether incomplete or wrong is a word choice, it doesn't change what's missing. So with each new discovery, our understanding improves, our wrongness decreases.

cnity 3y ago
> If we did know everything, then we would have an acceptable solution to all of our problems. Since we do not, it stands to reason that we don't know everything. This can be proven false by contradiction: it may be possible to _know_ that one of our problems has no solution.
- glitchc 3y ago
  > This can be proven false by contradiction: it may be possible to _know_ that one of our problems has no solution. This claim requires a bit more explanation, not sure if possible. Can you elaborate, or use an example?

ndsipa_pomu 3y ago

I think your use of infinity isn't particularly helpful here as it leads to the contradiction that knowing more doesn't lessen the knowledge gap, whereas it does appear to do so. Maybe, a better interpretation would be that as we learn and understand more, we approach the limits of knowledge. Now it may take an infinite amount of knowledge to actually reach the limits of knowledge (c.f. an infinite series can approach a finite value, but takes forever to get there), but it can still be shown that we are getting nearer. The other aspect is that as we understand more, we appreciate that there's even more to understand, but that can be thought of as our precision increasing and looking at the available knowledge in greater detail.

fnovd 3y ago
There is no contradiction because there is no limit of knowledge. The limit of y = e^x is infinity. You can keep increasing x and y will increase exponentially. So you plot the function, let's say with the x axis going up to 10 and the y axis going up to e^10. The graph shows very clearly that, while there was progress before, we have even more progress now. Exponentially more, even! What came before is dwarfed by what we have now; if you look at the range of y for x values 9-10 you can see how little of a difference all those others values (1-8) had between one another, compared to the changes we have now. The rate of change is so high that we're basically in an era of semi-complete knowledge. We must be at some kind of inflection point, this is truly a unique era of understanding. Then you repeat. Set the x axis to 100, and the y axis up to e^100. Oh wait, it's the same graph. That's because it's always the same graph. It's scale-invariant. The slope at every point is always whatever y is. We're always at right at the limit of explaining the "essential nature" of the universe because the "essential nature" of the universe can only be (to us) what we can understand it to be. We chose e^10 as the limit of the y-axis in our first exercise because that's all the knowledge we knew about. We chose e^100 as the limit of the y-axis in our second exercise because that, too, was all the knowledge we knew about. Choosing these random values as the limits of our function (i.e. the limit of the "essential nature of the universe") leaks information into the visualization that will always paint a picture showing that we're at the most transformative time there ever was. When we do it that way, we will always come to the same _wrong_ conclusion. We will always dwarf what came before and be dwarfed by what comes after. To think that we're actually living in an inflection point is hubris, it's wishful thinking, it's the sour grapes of mortality.