My objection lies with Terence's conclusions. As I said explicitly in my previous comment: perhaps Terence should have provided a counter proof to the mathematics he didn't approve of. By the way probability theory is an extraordinary tool for science. Many scientific developments rest on assumptions. Understanding where applications of theory break down due to those assumptions is important, but scientists don't throw the baby out with the bath water as Terence seems to.
@TeddyJohnson1990 This is a brief clip which does not go into much depth, however it seems as though Terence was using the incommensurability/incompleteness theorems as his logical foundation/proof. Is his summary of those theorems inaccurate, and if so so which part? Also, I'm a bit troubled by that last sentence; you make it seem as if Terence was calling for us to abandon probability theory and our current mathematics. He's merely trying to get us to demand more from our current systems.
@MakeItEmphatic Right, and so how might we "demand more from our current systems"?
Science/mathematics works by establishing a step logically and proceeding to another step only after proof that such a step is logically consistent. So where has this "system" failed? I am not asking how results could be erroneously extrapolated by someone that doesn't understand the full breadth of the logic, I'm asking where the system has intrinsically failed?
@TeddyJohnson1990 According to Godel, formal mathematical systems can produce unprovable statements, and the systems themselves are inherently incomplete/inconsistent. In Terence's mind, this means the system has failed to provide closure. We “demand more” by aspiring to create completely perfect logical systems. Probability theory's ability to merely show us all the potential possibilities is also not adequate, and we demand more by creating systems which actually predict events.
@MakeItEmphatic Probability theory helps us predict events, however it is impossible to guarantee an event will happen for certain unless it's probability is 1. To be able to predict the outcome of a random event with certitude one would essentially have to know everything there there is to know about the object or event in question. The Heisenberg uncertainty principle tells us this is not possible. i.e. we can give estimations or a "probability" that an event occurs.
I agree with you: given our current understanding of the world, there is no system of scientific inquiry which is able to predict future events with 100% certitude. But that's not what Terence is suggesting, he seems to be thinking hundreds of years down the line after our current systems have undergone a certain amount of refinement. Humans of the future may very well look upon probability theory and the heisenberg uncertainty principle as a crude stepping stones in human understanding.
@MakeItEmphatic Yes I completely agree. Generations into the future we may have a deeper understanding of space and time beyond our current perspectives. However probability theory continues to be a valuable tool that should not be discounted, especially since the uncertainty principle is a physical law.
@TeddyJohnson1990 Don't get me wrong, I do feel that current systems such as probability theory are extraordinarily useful enterprises. I just always keep myself aware of the provisionality of knowledge, and huge jumps that take us from geocentrism to heliocentrism. Scientific laws are constantly being updated after new discoveries are made. I've been hearing about this Quantum Memory Theory which challenges aspects of the uncertainty principle, but who knows if that will amount to anything.
@MakeItEmphatic That's pretty interesting. I'll have to check it out. Recently I saw an article on a result from CERN that seemed as though the neutrino could travel faster than light, however after further experimentation they concluded their original measurements off. If it were true though, many fundamental concepts in physics would have to be amended
This guy should have made a greater attempt at mathematics before discounting its logical foundations. This man is the product of extending a fallacious foundation to illogical conclusions. If he truly believes mathematics is irrelevant in its current form he should disprove the logical basis it rests on. GOOD LUCK.
@TeddyJohnson1990 If you have a moment, I'd like for you to inject a greater degree of specificity into some of the phrases you used, namely “fallacious foundation” and “illogical conclusion.” They're just extraordinarily vague, and I would appreciate if you could clarify. I'm just not sure whether you object to Godel's theorems, or to Terence's summation. I'd hardly say that Terence feels mathematics to be irrelevant; just concerned that Probability Theory is far too limited in scope.
My objection lies with Terence's conclusions. As I said explicitly in my previous comment: perhaps Terence should have provided a counter proof to the mathematics he didn't approve of. By the way probability theory is an extraordinary tool for science. Many scientific developments rest on assumptions. Understanding where applications of theory break down due to those assumptions is important, but scientists don't throw the baby out with the bath water as Terence seems to.
TeddyJohnson1990 2 months ago
@TeddyJohnson1990 This is a brief clip which does not go into much depth, however it seems as though Terence was using the incommensurability/incompleteness theorems as his logical foundation/proof. Is his summary of those theorems inaccurate, and if so so which part? Also, I'm a bit troubled by that last sentence; you make it seem as if Terence was calling for us to abandon probability theory and our current mathematics. He's merely trying to get us to demand more from our current systems.
MakeItEmphatic 2 months ago
@MakeItEmphatic Right, and so how might we "demand more from our current systems"?
Science/mathematics works by establishing a step logically and proceeding to another step only after proof that such a step is logically consistent. So where has this "system" failed? I am not asking how results could be erroneously extrapolated by someone that doesn't understand the full breadth of the logic, I'm asking where the system has intrinsically failed?
TeddyJohnson1990 2 months ago
@TeddyJohnson1990 According to Godel, formal mathematical systems can produce unprovable statements, and the systems themselves are inherently incomplete/inconsistent. In Terence's mind, this means the system has failed to provide closure. We “demand more” by aspiring to create completely perfect logical systems. Probability theory's ability to merely show us all the potential possibilities is also not adequate, and we demand more by creating systems which actually predict events.
MakeItEmphatic 2 months ago
@MakeItEmphatic Probability theory helps us predict events, however it is impossible to guarantee an event will happen for certain unless it's probability is 1. To be able to predict the outcome of a random event with certitude one would essentially have to know everything there there is to know about the object or event in question. The Heisenberg uncertainty principle tells us this is not possible. i.e. we can give estimations or a "probability" that an event occurs.
TeddyJohnson1990 2 months ago
I agree with you: given our current understanding of the world, there is no system of scientific inquiry which is able to predict future events with 100% certitude. But that's not what Terence is suggesting, he seems to be thinking hundreds of years down the line after our current systems have undergone a certain amount of refinement. Humans of the future may very well look upon probability theory and the heisenberg uncertainty principle as a crude stepping stones in human understanding.
MakeItEmphatic 2 months ago
@MakeItEmphatic Yes I completely agree. Generations into the future we may have a deeper understanding of space and time beyond our current perspectives. However probability theory continues to be a valuable tool that should not be discounted, especially since the uncertainty principle is a physical law.
TeddyJohnson1990 2 months ago
@TeddyJohnson1990 Don't get me wrong, I do feel that current systems such as probability theory are extraordinarily useful enterprises. I just always keep myself aware of the provisionality of knowledge, and huge jumps that take us from geocentrism to heliocentrism. Scientific laws are constantly being updated after new discoveries are made. I've been hearing about this Quantum Memory Theory which challenges aspects of the uncertainty principle, but who knows if that will amount to anything.
MakeItEmphatic 2 months ago
@MakeItEmphatic That's pretty interesting. I'll have to check it out. Recently I saw an article on a result from CERN that seemed as though the neutrino could travel faster than light, however after further experimentation they concluded their original measurements off. If it were true though, many fundamental concepts in physics would have to be amended
TeddyJohnson1990 2 months ago
This guy should have made a greater attempt at mathematics before discounting its logical foundations. This man is the product of extending a fallacious foundation to illogical conclusions. If he truly believes mathematics is irrelevant in its current form he should disprove the logical basis it rests on. GOOD LUCK.
TeddyJohnson1990 2 months ago
@TeddyJohnson1990 If you have a moment, I'd like for you to inject a greater degree of specificity into some of the phrases you used, namely “fallacious foundation” and “illogical conclusion.” They're just extraordinarily vague, and I would appreciate if you could clarify. I'm just not sure whether you object to Godel's theorems, or to Terence's summation. I'd hardly say that Terence feels mathematics to be irrelevant; just concerned that Probability Theory is far too limited in scope.
MakeItEmphatic 2 months ago
999th viewer i fell ashemed
breakingbenjaminguy2 5 months ago
i think he meant Kurt Godel's incompleteness theorem confusing it with incommensurability, either way they are related ideas anyhow
Mjze123 1 year ago
this is why math looked completely irrational/delusional during elementary-high school.
yoseph89 1 year ago
Comment removed
willthetuber 1 year ago