Insights I Know the Math Says so, but Is It Really True?

[russ_watters]

In order to have a scientific theory it must be falsifiable. That means that you must be able to make specific predictions about the outcome of experimental measurements whose result will either validate or falsify a theory. This is central to the scientific method. I see no way to do that without math.

Evolution was not a scientific theory in that sense for quite some time after it was developed.

I see no problem with that. Evolution is like "gravity" - it is primarily a name for an observed phenomena in nature. Darwin noticed the phenomena exists and came up with a partial explanation for how it worked. Which is great, but still limited.

But the predictions do not have to be quantitative - they can be simple observations.

I disagree. Even a "simple observation" can usually be made quantitative, e.g. X>0. I don't know what sort of valid scientific evidence would not be mathematical/quantitative.

So in your opinion, everything in the list below is quantitative, not qualitative?

https://en.wikipedia.org/wiki/Evidence_of_common_descent

How do you connect observations to hypothesis without at least some math? I see lots of math/implied math in that link. Let's be specific.

One key facet of evolution is how traits are passed along from parent to child. It's known that the same trait can be generated independently along different evolutionary paths. So just showing that two animals have the same trait doesn't prove they are related, much less make the relationship clear. But with genetics you can prove quantitatively how traits are passed down and figure out the actual links between species.

The simplest (simplistic/oversimplified) common first example is eye color: One parent has blue eyes and the other brown. What are the odds of their kids having blue/brown eyes? This may be easy math, but its math nonetheless.

 

[BillTre]

[Moderator's Note: Most of the content in this post has been moved to a new thread:

https://www.physicsforums.com/threa...ion-and-blood-circulation.994788/post-6404335

Moved content has been deleted below.]

Hmm, I think you are confusing feasibility with falsifiability. For example, even before the technology to detect gravitational waves was developed, the existence of gravitational waves was a falsifiable prediction.

If LIGO did not find gravitational waves, would that have proven they don't exist? (I am not convinced, maybe it wasn't sensitive enough).

You appear to not recognize that different models make different specific predictions about the energy range of a given particle. If they do not see it in a particular range then yes they will continue looking elsewhere, but that non-observation already eliminates some of the theories.

Do you really want to restrict all science to be dependent upon using math?

• Not all data has to be presented as math,
• Not all advances in science have been driven strictly by hypothesis testing
• There are inductive methods that don't require (but of course can use) math

 

[PeterDonis]

Do you really want to restrict all science to be dependent upon using math?

Nobody is saying that any time anyone does any kind of science, they have to use math.

We are saying that, in order to compare the predictions of a scientific theory with data and thereby establish whether the theory is falsified or confirmed, you need to use math.

Please focus discussion on that specific claim instead of responding to straw main claims that nobody is actually making.

 

[BillTre]

We are saying that, in order to compare the predictions of a scientific theory with data and thereby establish whether the theory is falsified or confirmed, you need to use math.

What I wrote about analyzing phylogenetic trees using methods like cladistics in fact can do this.

Please focus discussion on that specific claim instead of responding to straw main claims that nobody is actually making.

This is not a straw man claim.
It can certainly be done math free (in simple cases).
You seem to be ignoring it, but it directly refutes this claim.

 

[PeterDonis]

What I wrote about analyzing phylogenetic trees using methods like cladistics in fact can do this.

With math, yes, as @Dale has already pointed out.

This is not a straw man claim.

The claim you are making now, which appears to be simply that some scientific theories can so have their predictions compared with data without using math, is not responding to a straw man claim, no.

But you have shifted your ground from what I quoted from you before. Before, you were claiming that we are saying nobody can do any science at all without using math. "Do any science at all" is much broader than "compare the predictions of a scientific theory with data". Nobody has made any such claim, so that claim is a straw man. If you are no longer saying anyone has made such a claim, good.

It can certainly be done math free (in simple cases).

So far you have failed to give any case which can be done math free; every example you have proposed has been refuted.

 

[PeterDonis]

If LIGO did not find gravitational waves, would that have proven they don't exist?

No, because we already had other indirect evidence for gravitational waves: observations of the orbital parameters of binary pulsars changing over decades, for example. Those observations were consistent with GR predictions for how orbital parameters of such systems should change over time due to gravitational wave emissions. If those observations had been different, GR's model of such systems would have been falsified.

And the comparison of observations with predictions of course required math.

 

[russ_watters]

I feel like the search for vague yet specific examples of qualitative science has at best inadvertently conceded the point. If 500 years ago we could have said "species evolve" or "apples fall" and called them scientific predictions, that doesn't provide much value or hold much relevance to the modern scientific process. Today we model/prove such things with math/mathematical logic.

Also, I'll claim that the value of the "softer" sciences is still best expressed/proven with math. Behavioral sciences come to mind, there. The fact that they are often practiced without it is more a bug than a feature.

 

[Jarvis323]

I don't see why. Knowing enough about the subject matter of a theory to know whether one is interested in it, is a lot easier than knowing enough about the details of the math to have a valid opinion, based on your own knowledge, about whether the theory is correct.

The target audience is all PF members. The article is not trying to persuade anyone of anything.

And you are, of course, entitled to your opinion. But note that your opinion stated here is not about any scientific theory, but about a non-scientific statement that I made--basically, my opinion, which is also not about any scientific theory. So neither of those opinions fall into the category I was talking about in the article.

This is not a substantive response. I have been making specific arguments, and so have others. Vague complaints are not a valid response to specific arguments.

I'm confused. So this is a thread about a vague (not necessarily) persuasive opinion about what a valid opinion is? And now we are trying to make it clear enough to have a debate about it with valid arguments?

 

[PeterDonis]

So this is a thread about a vague non-persuasive opinion about what a valid opinion is? And now we are trying to make it clear enough to have a debate about it with valid arguments?

Please read my posts in context. The last quote you gave was in a particular subthread, in which you are not currently participating, about a particular scientific theory being discussed (evolutionary theory). The other quotes were in response to you in a different subthread which was about the topic of the article as a whole.

 

[PeterDonis]

I'm confused.

So am I. Do you have particular points to make and you're not sure whether they are appropriate to make in this thread? If that's not the case, I'm not sure what the point of your remarks is.

 

[Jarvis323]

So am I. Do you have particular points to make and you're not sure whether they are appropriate to make in this thread? If that's not the case, I'm not sure what the point of your remarks is.

It's just ironic, that the thread is about an opinion of what a valid opinion is. The OP opinion was not intended to be persuasive, which seems to imply it wasn't constructed with valid arguments (at least not deliberately). So we are left with a presumably invalid opinion about what a valid opinion is. And this has stemmed a debate that is now to the point of requiring valid, persuasive arguments. I don't even think we've laid down any definitions yet. It's kind of an ironic mess. Maybe we should be using math instead of natural language to figure this all out?

 

[Jarvis323]

Seriously though, if I am to weigh in on the sub-thread debate, I think there is a constantly shifting goal post. First someone was arguing that some scientific fields are largely or predominantly qualitative. And now it's about whether any math at all is required in those fields. To me there seems to be truth in both. It seems like people are now just competing against one another to claim a victory rather than to develop insight.

 

[PeterDonis]

@Jarvis323, all I can really glean from your posts is that you disagree with me. Ok, noted.

 

[Jarvis323]

@Jarvis323, all I can really glean from your posts is that you disagree with me. Ok, noted.

Not really, I guess I'm just trying to point out what I think has gone wrong in this thread. You're one of the best physicists at PF, and I rely on your opinions frequently, especially about new physics theories and such. I basically agree, or rather I gain some insight from what you are saying, and also from what the people debating you are saying. Without precise definitions and clear logical arguments though, it's all just opinion. There is middle ground, not everything is black and white, and nobody needs to come out of the discussion as the victor.

 

[PeterDonis]

I guess I'm just trying to point out what I think has gone wrong in this thread.

I don't think anything has "gone wrong". This is a General Discussion thread, and that's what we are having, a general discussion based on the general topic of the article.

Without precise definitions and clear logical arguments though, it's all just opinion.

Yes, that's what tends to happen in General Discussion threads.

Perhaps you are confused by the fact that this is a comment thread on an Insights article, and those are more typically in one of the physics subforums. That's because most Insights articles are about particular physics topics where the point of the article is to give the current mainstream science on the topic, not to just express the author's own opinions. This article is unusual in that it is the latter, not the former; but that's why the discussion thread is in General Discussion.

That does raise another point, though: the specific subthread you quoted from is about a more specific topic that arguably should be spun off to a separate thread in one of the science subforums. I'll bring that up with the other moderators.

 

[PeterDonis]

the specific subthread you quoted from is about a more specific topic that arguably should be spun off to a separate thread in one of the science subforums. I'll bring that up with the other moderators.

After discussion, the subthread referred to above has been moved to a new thread in the Biology forum:

https://www.physicsforums.com/threa...-data-evolution-and-blood-circulation.994788/

 

[bhobba]

I am reading Wittgenstein's Lectures on Mathematics right now:
http://positivists.org/blog/archives/5425

In it there is a debate between Wittenstein who thinks mathematics is just a convention, not actually about anything, and Turing who thinks mathematics is about reality and if it wasn't correct bridges would fall down etc. I think when used in applications it is about models that use mathematical concepts. The logical consequences are tested experimentally to determine if it is a good or bad model. Models are neither right or wrong - simply in good accord with experiment or not. Arguing about what the things in the models are ie reality or just a convention is equally as useless as arguing what reality itself is - philosophers like that sort of thing - but scientists mostly are not that interested. That it will lead nowhere seems pretty common. Feynman's views are quite prevalent. The easiest answer IMHO is models are the best description we have of reality. We can describe reality, but what it actually is - who knows. Guys like me would also say - who cares - that we can describe it is the best we can do - whether we use math or english. Asking - I know the math says so - but is it really true is not a good question. Much better to ask - I know the math says so - but is it in accord with experiment ie is it a good model or not.

I know in discussing science we use concepts like right or wrong - real or not real - and even think physics may be heading towards an ultimate truth. That's fine in everyday speech, which is full of 'sloppiness', and people generally do not get confused or worried. But when looked at carefully all sorts of issues arise that require care in answering.

Thanks
Bill

 

[bhobba]

I don't see the problem with some individual not believing something in physics. Anyone is free to disbelieve. Why not?

Of course. But you are not free to be unchallenged, nor for people to consider it equally as valid as theories in accord with experiment.

Thanks
Bill

 

[BWV]

Against my better judgement, here is another quibble to
"If you don’t understand the math, you’re not entitled to an opinion about the theory."

The piece does a good job of attacking 'common sense' or pop-science arguments against standard physical theories, however it completely possible to have an informed opinion on complex ideas in mathematical physics without knowing the math. You can not do physics without mastering the math, but you can be an informed observer. The corollary to the 'not entitled to an opinion' argument is that the people who actually fund and hire scientists cannot evaluate the fruits of their investment? Good science journalists must have PhDs in physics to knowledgably write on the topic?

For example, there are two answers to the question in the article
I don’t understand how black holes can actually exist. Doesn’t it take an infinite time for anything to fall in?

1: Learn the math of GR and really understand the issue
2:Trust science as there is no debate among physicists who do understand the math and the theory is over 100 years old, just accept it is so.

If you use the word 'opinion' literally, it is defined as
a view or judgment formed about something, not necessarily based on fact or knowledge.

Can anyone, scientist or layman, really have a valid opinion on General Relativity? What is there to have an opinion about? If it is math, then you might as well ask someone's opinion on the associativity of addition. The only areas where one can have an opinion are issues currently disputed within science. There I can develop a quite informed opinion on a disputed hypothesis, MOND for example, from good science journalism which focuses on key points of contention, some of the experimental evidence for and against and how well the model is accepted relative to others. Of course I won't understand it well enough to be able to add anything to the debate within physics, but that is not what 'having an opinion' means.

 

[PeterDonis]

it completely possible to have an informed opinion on complex ideas in mathematical physics without knowing the math

I assume you mean this:

2:Trust science as there is no debate among physicists who do understand the math and the theory is over 100 years old, just accept it is so.

That is not having an informed opinion. That is accepting the word of someone else on their authority.

Can anyone, scientist or layman, really have a valid opinion on General Relativity? What is there to have an opinion about?

Whether or not GR is an accurate scientific theory: whether it makes accurate predictions in its domain. Having an informed opinion about that means being able to check those predictions for yourself, instead of just taking someone else's word for it when they claim the predictions are accurate.

 

[PeterDonis]

the people who actually fund and hire scientists cannot evaluate the fruits of their investment?

In many cases, no, they can't. Many people who fund and hire scientists have no idea whether or not the science those scientists are doing makes accurate predictions. They are not funding the scientists to get accurate predictions from them; they are funding the scientists for other reasons, such as prestige or politics.

Good science journalists must have PhDs in physics to knowledgably write on the topic?

No. I have nowhere claimed that having a PhD is either necessary or sufficient for having an informed opinion about a scientific theory, nor has anyone else in this thread. You are attacking a straw man.

That said, I think it is true that most science journalists do not have informed opinions on the topics they write about; they are just accepting the word of their favorite scientists as authoritative.

 

[MikeeMiracle]

Going back to the original post I have a slightly different viewpoint. As someone who doesn't understand the maths, I am perfectly happy accepting that I cannot have a "full picture" understanding of the events at hand without a detailed maths knowledge. What I try and do is compile information from various sources, learning concepts from pop-sci videos (PBS Spacetime / Science Asylum type level)and then reading about them on PF to fill out the picture as much as possible which as worked very well for me. In my opinion I feel I have a "better than most" people's understand of concepts based on the "plain english" explanations.

What frustrates me are the posts where we have people asking questions on concepts. They appear to struggle to understand the concepts so they receive replies stating that "if they knew the maths it would make sense" only for them to reply that "they have studied and understand the maths, can perform the required calculations"...but struggle with the concepts still.

I would love to get a grip on the maths behind the concepts and feel some envy that they understand the maths where I do not yet they don't seem to understand the concepts.

I just don't get it!

 

[bhobba]

I just don't get it!

Susskind is doing his best with the Theoretical Minimum series of books. He has done 3 already - but none for a while. I do hope he finds the time to finish them. Here the general public will find a correct account, but they must be willing to put in the effort to understand a bit of calculus. At the end though they will understand things far better than the usual pop-sci accounts. As to what the concepts mean, when using the language of math, you will find most of the time that is all that is needed. Going beyond that can, and often is, hard.

Thanks
Bill

 

[BWV]

How many hours of study does it take to become proficient in, say, QFT at a professional level? Thinking one can casually learn these topics is like believing that tinkering on the piano a few hours a day can make you a concert pianist. I watched the Susskind Stanford videos years back and they were great, but after that, I did not 'know' these topics, but I understood better what I did not know

 

[gmax137]

Thinking one can casually learn these topics is like believing that tinkering on the piano a few hours a day can make you a concert pianist.

Well that's an interesting observation. I have enjoyed music my whole life without ever playing piano, guitar, or anything. I believe musicians appreciate some of the details more than I do. But, nobody is promoting the idea that concert-going is a waste of time for non-musicians.

 

[BWV]

Well that's an interesting observation. I have enjoyed music my whole life without ever playing piano, guitar, or anything. I believe musicians appreciate some of the details more than I do. But, nobody is promoting the idea that concert-going is a waste of time for non-musicians.

Indeed, the analogy is the more you learn about music as a listener or amateur musician, the more appreciation you have for people who do it at a very high level

 

[bhobba]

How many hours of study does it take to become proficient in, say, QFT at a professional level?

You mean after you have done something like Susskind? Well he claims to take you to a level where you at least understand the jokes. To take you to more advanced QM that would be about 1 university course which is about 150 hours. Then 2 subjects on QFT or a further 300 hours. But it depends on how hard you find Susskind. If it was about average difficulty for you then I would say that 450 hours is reasonable. Let's be generous about this and you study about an hours per day with weekends free - then I would say about 2 years.

But if you are interested in professional level understanding you will be better going to university for a graduate degree like the following:
https://my.uq.edu.au/programs-courses/plan.html?acad_plan=PHYSCX2321

That will also take about 2 years part time - but with about 2-3 hours study each night.

Thanks
Bill

 

[BWV]

[

You mean after you have done something like Susskind? Well he claims to take you to a level where you at least understand the jokes. To take you to more advanced QM that would be about 1 university course which is about 150 hours. Then 2 subjects on QFT or a further 300 hours. But it depends on how hard you find Susskind. If it was about average difficulty for you then I would say that 450 hours is reasonable. Let's be generous about this and you study about an hours per day with weekends free - then I would say about 2 years.

But if you are interested in professional level understanding you will be better going to university for a graduate degree like the following:
https://my.uq.edu.au/programs-courses/plan.html?acad_plan=PHYSCX2321

That will also take about 2 years part time - but with about 2-3 hours study each night.

Thanks
Bill

but that would assume a good foundation in basic physics and math, if your only introduction to classical mechanics was Susskind, that would likely not be a good enough foundation. Also there is a large gap between understanding the math conceptually, which is really what Susskind requires, vs being proficient at using the math to solve problems. Then once you get there, its ‘use it or lose it‘ otherwise you will just forget it all

 

[bhobba]

but that would assume a good foundation in basic physics and math, if your only introduction to classical mechanics was Susskind, that would likely not be a good enough foundation. Also there is a large gap between understanding the math conceptually, which is really what Susskind requires, vs being proficient at using the math to solve problems. Then once you get there, its ‘use it or lose it‘ otherwise you will just forget it all

Susskind covers a lot more than just classical mechanics. Of course it depends on your preparation and what you recall. If you just read Susskings 3 books then yes I think one hour each night for 2 years is enough. If you did a degree with not much math, or do not remember much, then a prior diploma in math would be of value:
https://my.uq.edu.au/programs-courses/plan.html?acad_plan=MATHEX2321

That would take it to 3-4 years. But you are asking for professional level knowledge. Really is that want you want - or just to get the jokes as Susskind says. That's all the general citizen really needs.

Thanks
Bill

 

[swampwiz]

I had thought that someone falling into black hole would have time being so dilated from the mass that he would observe the universe evolving very rapidly, even to the point of seeing stars form, go into giant phase, supernova, etc. very quickly; OTOH, anyone observing him would observe his watch as almost not ticking at all.

 

[PeterDonis]

I had thought that someone falling into black hole would have time being so dilated from the mass that he would observe the universe evolving very rapidly, even to the point of seeing stars form, go into giant phase, supernova, etc. very quickly

No, this is not correct. An observer hovering at a constant altitude above the hole's horizon, not falling in, will see what you describe. But an observer free-falling into the hole will actually see the outside universe redshifted, not blueshifted, with the redshift increasing as he falls.

OTOH, anyone observing him would observe his watch as almost not ticking at all.

This is correct (at least as long as the observer is outside the horizon, so light signals from him can get back out to distant observers). But that is because, for an observer free-falling into the hole, the time dilation between him and an observer who is far away is symmetric, like time dilation in SR--each observer sees the other's clock running slow. This is a key difference between this case and the case of a hovering observer.

 

[LieToMe]

Why are people making this weird assumption that "math" says anything? People are the ones making arguments. No matter what you write it will only ever be an approximation of relative observations. The only reason we take an interest in it is for practical applications in being able to predict the evolution of systems to some arbitrary degree of certainty in some arbitrary consideration of variables.

People happen to choose some level of tolerance in the statistical correlation of their measurements and there happens to be a relativistic space-time model with the highest correlation to patterns we observe in astronomical objects. According to our best understanding of the standard model, it is astronomically unlikely that the pattern of observations can be explained by a capacity to measure "infinite" time, so the point was moot to begin with, just like asking for the frame of reference of a photon.

 

[romsofia]

Why are people making this weird assumption that "math" says anything?

Why do people make this weird assumption that "English" says anything? People are the ones who give words meaning. No matter what you write it will only ever be an approximation of how society interprets it. The only reason we take an interest in it is so for practical applications in being able to communicate with others to some arbitrary degree of certainty in some arbitrary consideration of intent.

People happen to choose some level of tolerance in the statistical correlation of their definitions, and there happens to be a book with the highest amount of definition to words we observe in society. According to our best understanding on English, one cannot define "the point of LieToMe's post" so the point was moot to begin with, just like asking for the definition of the word "obagooba".

 

[LieToMe]

Why do people make this weird assumption that "English" says anything? People are the ones who give words meaning. No matter what you write it will only ever be an approximation of how society interprets it. The only reason we take an interest in it is so for practical applications in being able to communicate with others to some arbitrary degree of certainty in some arbitrary consideration of intent.

That's something I've actually found to be true. Even now, all we have are statistical measurements, so to a certain degree, you can't be entirely certain about anything. That inability to be entirely certain is how scientific models appear to perpetually evolve.

You can make an argument that logic is independent of observable results, but then such an assumption would only be relative to an individual's construct of reality as a reiteration of past interactions.

 

[Imager]

As one of the people who haven't taken the time to understand the math, I think Peter's points are correct. When I first came to this site, one of my big problem was not getting simple answers like "Youtube" videos.

My other big problem was terminology. For example, using the term universe when they mean observable universe. It took me a while to figure out that those where different things. It's hard for us to ask the right questions, when we don't even understand the differences in terminology.

What makes this forum Great is that people like @PeterDonis, @Dale and many others showing massive amounts patience to walk people like me through the basic concepts!

 

[joeh3rd]

The mathematical models you refer to in other disciplines are still subject to the same test as mathematical models in physics: either they make predictions that match the data, or they don't. Models that don't make predictions at all aren't the kind of "math" I am talking about in the article.

Also, your post implies that mathematical models in physics don't have the characteristics you describe--simplifying complex processes, modeling domains where inputs are not fully knowable. That is quite wrong. There are plenty of domains in physics where the same issues arise. In fact, it's hard to find a domain even in physics where those issues don't arise.

Perhaps there is an example of predictive models containing non-existent or at least non-intuitive features. In electrical engineering Fourier transforms and convolution are used extensively in radio transmitter and receiver design. The heterodyning used for frequency shifting of modulated signals up for transmission and down for audio routinely use the negative frequency component of frequency shifting. I don’t believe that there have been tests for the existence of such however in application they are definitely present as symmetrical side bands of upshifted modulation.
Here we have a mathematical construct that emerges in transformation from the time domain to the frequency domain and back again that works mathematically but has a seemingly non-detectable real world component. Are we sometimes taking a mathematical model that when used may have non-existent internal characteristics yet when used in a series of operations yields measurable results and mistakenly assuming it is what occurs in reality?
Perhaps “virtual particles” are the same just as for modeling purposes we assume the atomic model and things called particles which may be side-effects of our means of measurement and perception — no tiny balls that behave similar to things we perceive by immediate sight and other senses on a much larger scale?

The positive frequency side of a modulated signal. More properly shown, it is symmetric when along the zero frequency axis.

The result when frequency shifted by multiplying with a sinusoid centered at 30kHz. Note the formerly negative frequency lower side and.

 

[PeterDonis]

I don’t believe that there have been tests for the existence of such however in application they are definitely present as symmetrical side bands of upshifted modulation.

You're contradicting yourself. First you say there are no tests for the existence of such, then you say they are definitely present. They can only be definitely present if we have a way of testing for their presence, and the test says they are. If the test is "symmetrical side bands of upshifted modulation", then if those things are present, "such" is present.

Are we sometimes taking a mathematical model that when used may have non-existent internal characteristics yet when used in a series of operations yields measurable results and mistakenly assuming it is what occurs in reality?

In order to even ask this question, you must assume that you can somehow distinguish "non-existent internal characteristics" from internal characteristics that aren't "non-existent". But that would require some kind of experimental test for such characteristics, and if such a test exists, the characteristics aren't "internal" to begin with.

 

[Tommy White]

Continue reading...

Makes me think of what Feynman sais here:



(Of course there are theoretical physicists and mathematical physicists though. A lot of physics can be explained by using just words, but none to apply it.)

 

[Tommy White]

Makes me think of what Feynman sais here:



(Of course there are theoretical physicists and mathematical physicists though. A lot of physics can be explained by using just words, but none to apply it.)

I meant this as a reaction to the article, I didn't knew there was a whole conversation about it where this comes from out of nowhere I image. (Thought I might had to clarify that just in case.)

 

[zdcyclops]

Continue reading...

Interesting.
Einstein is reported as having once said " If you can't explain it to a six year old, you don't understand it." Mathematics is no more special than any other creation of the human imagination.
The universe does not calculate, does not use mathematics, yet everything seems to work quite well without it.

 

[Dale]

Einstein is reported as having once said " If you can't explain it to a six year old, you don't understand it."

It is probably misattributed: http://en.wikiquote.org/wiki/Albert_Einstein#Misattributed

But even if it were correctly attributed it is wrong. Teaching a concept clearly and understanding it are two different skills

 

[strangerep]

The universe does not calculate, does not use mathematics, yet everything seems to work quite well without it.

Heh, the universe is one big analog computer.

 

[Klystron]

Mathematics is no more special than any other creation of the human imagination.

Arguably incorrect.

Tinker Bell is a special creation of the human imagination. As much as I like Tink and clapped my hands hard so she would get well, mathematics remains far more useful and special.

The universe does not calculate, does not use mathematics, yet everything seems to work quite well without it.

Of several logical fallacies inherent in this statement, an existential 'least' refutation may be simplest.

1. Human beings exist in (are part of) the universe.
2. Humans count, calculate and use mathematics.
3. Therefore, (part of) the universe calculates and uses mathematics.

 

[HAYAO]

Excellent article.

Yeah, I was on the both ends of this. When I was young and had no good mathematical intuition of a physical phenomenon, I was really frustrated. Now, as an assistant professor, I get frustrated when people don't understand the mathematical representation of physical phenomena.

I still do think that almost all, if not all, physical theories are based on certain postulates. These postulates are based merely on physical intuition, although a good one. For example, one of the postulates of special relativity is that speed of light is constant in vacuum. No one can really "prove" this, but it is based on a good reasoning and observation if anything else. And since the theory of special relativity reflects the real world and it works, we "assume" that the postulates are correct. Similar thing for wave representation of particles. We assume that the particle behaves like a probability (amplitude) wave function, but the theory based on this actually works and reflect what we'd expect to observe. The more we do experiments and the more we have stronger mathematics to dig deeper into this, the more it reinforces the theory or provide a more generalized theory that encompasses all the other theories (e.g. QM and QFT).

In many cases, mathematical representation of physics is a well-thought-out reasonable modeling/interpretation of the observed phenomena. If any student is doubting the math, it's not necessarily because they don't agree with math, but because they don't agree with the modeling/interpretation, due to lack of intuition (which can be trained to a certain extent; it's why people learn to accept it).

 

[Hornbein]

The math for general relativity was already known. The difficulty was discovering and showing that it related to the real world.

 

[bhobba]

The math for general relativity was already known. The difficulty was discovering and showing that it related to the real world.

As Hilbert, who discovered the GR equations slightly before Einstein (by five days), said: "Every boy in the streets of Gottingen understands more about four-dimensional geometry than Einstein. Yet, despite that, Einstein did the work, not the mathematicians."

Thanks
Bill

 

[weirdoguy]

If you can't explain it to a six year old, you don't understand it.

As a teacher, I think that is one of the stupidest things I have ever heard in my whole life.

 

[Hornbein]

As Hilbert, who discovered the GR equations slightly before Einstein (by five days), said: "Every boy in the streets of Gottingen understands more about four-dimensional geometry than Einstein. Yet, despite that, Einstein did the work, not the mathematicians."

Thanks
Bill

Einstein and his collaborator (Rosen?) were stuck so he went to Gottingen for help. He was quite loathe to do this. He said Gottingen had a reputation for stealing the results of others. Nevertheless out of desperation he made the trip. He was informed that he was trying to do the impossible, that one of the conditions he thought essential actually wasn't, and he already had the answer. Hilbert published his solution, which greatly angered Albert. He got Hilbert to back down and recognize AE's priority. I imagine it helped that Albert had the backing of Berlin.

 

[bhobba]

He got Hilbert to back down and recognize AE's priority.

In public at least, and likely in private, Hilbert always gave Einstein credit for GR. Of greater interest was when Einstein, Hilbert and others discovered solutions that violated energy conservation. Both were stumped. But they knew one person they thought could tackle it - the great Emmy Noether. And her famous theorem was borne. It may even be a more important discovery than GR. IMHO, it was just a precursor to modern science, which is very collaborative. The idea of the lone genius that could revolutionise science was fast fading.

As Wigner said of Einstein:

'I have known a great many intelligent people in my life. I knew Planck, von Laue and Heisenberg. Paul Dirac was my brother-in-law; Leo Szilard and Edward Teller were among my closest friends; and Albert Einstein was a good friend. But none of them had a mind as quick and acute as von Neumann. I have often remarked this in the presence of those men, and no one ever disputed me. But Einstein's understanding was deeper even than von Neumann's. His mind was both more penetrating and more original than von Neumann's. And that is a very remarkable statement. Einstein took extraordinary pleasure in invention. Two of his greatest inventions are the Special and General Theories of Relativity, and for all of von Neumann's brilliance, he never produced anything as original.'

Even the great Feynman, himself like Einstein beyond genius at the level of a magician, said knowing what Einstein did, he could not have invented Relativity. Ohanian has said such people are sleepwalkers. They did not know where they were going but were unerringly led there. Einstein was perhaps the greatest sleepwalker there ever was, except maybe for Newton.

Thanks
Bill

 

[Dale]

they knew one person they thought could tackle it - the great Emmy Noether. And her famous theorem was borne. It may even be a more important discovery than GR.

I agree 100%. IMO it is the single most important theorem in all of physics.