I think this is the wrong question to ask. We know what we want (a consistent foundation for calculus) and we think we know how to get it (with real numbers and infinite sets). But real number might not be the answer.

I think a much better question to ask is 'can we build a consistent foundation for calculus without real numbers and infinite sets?' I believe the answer is yes. Now, this doesn't imply that the alternative requires scrapping everything about real numbers. For example, I believe the alternative would have still have the area of a unit circle being pi, it would just mean something different. — Ryan O'Connor

This is a bit speculative without some sort of indication or hint of specifics. For example as I mentioned, I've looked into constructivism a bit, which is enjoying a modern resurgence due to the influence of computer science and computerized mathematical proof assistants. But you would reject even that.

Like the real numbers, the fundamental objects of the hyperreals are points/numbers. A continuum is constructed by assembling infinite points, each with a corresponding number. And so the hyperreals gets no closer to answering the question 'how can a collection of points be assembled to form a line?' I haven't investigated the constructivists' methods to produce an informed comment but from what I've seen it looks like more of the same. Points/numbers are treated as fundamental.

I don't have a formal theory but I do have an intuition on how the alternative would look. In line with Aristotle's solution to Zeno's Paradox, my view has continua (not points) being fundamental. — Ryan O'Connor

Sounds like a Peirceian viewpoint, about which I don't know much. But why am I supposed to be burdened for finding a mathematical viewpoint other than the standard one accepted by almost all the world's mathematicians except for those pesky constructivists and rare finitists and ultrafinitists? Why is this my problem, or math's problem?

I think the mathematics of calculus would be almost entirely unaffected in moving to a continuum-based view, but before we could even talk about it, you'd have to first be open to (at least temporarily) shedding your point-based biases and look at graphs in a new light. — Ryan O'Connor

You're just waving your hands.

I would love to hear your criticisms on my earlier post to you where I drew the polynomial in an unorthodox way. — Ryan O'Connor

I suppose I owe you that. I'm going to find it depressing and frustrating but I'll take a run at it sometime.

I am not well versed beyond such basics as that, so for more on the subject I recommend the Stanford article and the passages in the Church book. — GrandMinnow

Thank you for the references. Your post actually gave me a glimmer of understanding as to what @Metaphysician Undercover is talking about. And for that matter, what I'm talking about.

'2+1' and '6-3' are different terms, so, even though extensionally they name the same number, — GrandMinnow

I don't understand intensional versus extensional with respect to math (or anything else for that matter) but I've been trying to explain to @Metaphysician Undercover for two years that 2 + 2 and 4 refer to the exact same mathematical object. Without success, of course, but never mind that.

Can you briefly explain to me what that means? How you can use the concepts of intensional and extensional to make the point that 2 + 2 and 4 are two names for the exact same thing?

the terms themselves have different intensional meanings. — GrandMinnow

Ah maybe this is a clue. @Meta keeps saying to me (at least before we stopped discussing the issue) that 2 + 2 refers to the process of adding two things together; and 4 refers to a single thing. Therefore they don't have the same meaning. So that must be "intensional" as you say.

I've heard these two terms for years without understanding. And also intentionality with a 't', that's Searle's point that the Chinese room doesn't have intentionality, or "aboutness." I gather this is an entirely different concept than intensionality with an s?

You and Bartricks claim that either you-all, or other people, are locked down. Maybe in China. But I am specifically unaware of anyone anywhere being locked down, I submit to you your florid language has contaminated your thinking, making of it a foul thing on a philosophy site. Or maybe you just plain do not know what "lock-down" means. So what is it? Ignorance? Or something worse? — tim wood

You're the one getting foul, as shown by your initial response. And if you don't think there have been lockdowns in the US in the past year you're either lying or ignorant. There haven't been lockdowns? We've seen people get arrested for surfing alone, hiking alone, driving alone, being too far from home alone in their car. We've seen multiple stories of cops beating people up for not wearing their mask or even for wearing their mask "improperly." I could link you a dozen such stories without trying very hard. Just this very morning a woman was arrested for refusing to wear her mask in a bank in Texas, which has just repealed its mask law. A 65 year old woman. It's beneath you to post in such a disingenuous manner. This conversation is not productive.

But here are some more links.

The WSJ thinks there were lockdowns, why don't you take your delusions and gaslighting to them?
https://www.wsj.com/articles/the-lockdowns-werent-worth-it-11615485413?mod=djemalertNEWS

https://thefederalist.com/2021/03/12/democrats-are-sacrificing-american-kids-lives-to-get-more-power/

https://www.propublica.org/article/the-lost-year-what-the-pandemic-cost-teenagers

https://reason.com/2021/03/11/stop-trying-to-create-a-zero-risk-society-covid-19/

https://amgreatness.com/2021/03/11/one-year-later-vindication-for-lockdown-skeptics/

My view is that actual infinity should not be permitted in math any more so that than it is permitted in physics, but that's just my view and it's contrary to contemporary math so I'm willing to leave it at that. — Ryan O'Connor

I think we're done then.

Just out of curiosity though, how do you develop a theory of the real numbers without infinite sets? Even the constructivists allow infinite sets, just not noncomputable ones.

switched to a quantum sensor. With an SLR camera I agree that every photo has some degree of blurriness, but with quantum sensors that's not necessarily the case. There is no law which states that we can't know the position of a particle with perfect precision.


Also, I don't think particles are points, but instead excited states of quantum fields. — Ryan O'Connor

[/quote]

We're just not having the same conversation.

Forget about cameras, sensors, and speedometers - it all boils down to the question of whether a line can be constructed by assembling points. — Ryan O'Connor

The question doesn't come up in math. We use the phrase "the real line" as an alternate way of saying, "the set of real numbers," but everything can be done without reference to geometry.

Your earlier post indicated that you agree that this is a mystery (given the orthodox views)? Why not consider alternate views? — Ryan O'Connor

If I see a coherent one presented I'll engage with it. In the past I've engaged extensively with constructivists on this site and learned a lot about the contemporary incarnations of that viewpoint.

I've also studied the hyperreals of nonstanard analysis. So in fact I'm very open to alternative versions of math, but I don't see that you've presented one. The problem with finitism is that you can't get a decent theory of the real numbers off the ground.

Are tangent and instantaneous rate of change not the same thing? — Ryan O'Connor

No they're not. In functions from the reals to the reals (ignoring the multivariable case where this terminology doesn't make sense) the instantaneous rate of change is the slope of the tangent line.

If you reject the notion of instantaneous rate of change, how can you not reject the notion of tangents? — Ryan O'Connor

I don't, you and @Meta do. I'm agreeing that IN REALITY there may not be such a thing. But in math, there most definitely is. Again. you are equivocating math and physics. I'll stipulate to @Meta and your point that instantaneous rates are murky in physics. In math they're perfectly well defined.

I'm talking about mathematics. I understand that 0.333... converges to 1/3, but it is only (a useful) convention which states that convergence and equality are the same. If you're saying that it's proved somewhere that the two terms are equivalent then let's leave it at that. — Ryan O'Connor

You can't maintain your credibility while arguing against freshman calculus. here's the proof "somewhere," a somewhere I already linked to earlier.

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

The Stern-Brocot string for any rational number has finite characters. I don't accept the claim that that LL = LLLRrepeated since LL corresponds to a position in the tree and LLLRrepeated corresponds to a path along the tree. However, let's not waste any more time on 1/3. — Ryan O'Connor

On the contrary, 1/3 is the critical case here. If you can't agree that 1/3 = .333... then you fail freshman calculus and high school algebra too. There's nothing more to talk about then.

As with your speedometer argument, your addition of a shutter only complicates the issue without providing any further explanatory power. We add a shutter to cameras only to limit the amount of light that the film is exposed to. Without a shutter we can (at least in principle) still take photographs. Remove the shutter and the instant the first photon hits the film we have a photograph. — Ryan O'Connor

You know you keep making claims totally contrary to photographic technology. A single photon is not sufficient to make an impression on any film stock or digital sensor in existence. So you're just flat out wrong here. And if you don't open shutter at all, no photons will come in; and to get sufficient photons in to make an impression on a light-sensitive medium, you need to keep the shutter open for a period of time. Of course I include an electronic shutter that merely activates the sensor for a period of time.

And if no further photons hit the film we have an image with absolutely no blurriness. — Ryan O'Connor

There are no single-photon detectors outside of physics labs. But again, I don't know why you're belaboring this point. If you don't think that 1/3 = .333... AND you agree that you are making a mathematical point, then there is no conversation to be had. You're just wrong. Read a calculus book or work through the proof I linked (twice now) on Wiki.

This image captures no motion. It is not a video by any definition. I was anticipating you challenging the practicality of such a photograph, which is why I went quantum, but perhaps that's not necessary. — Ryan O'Connor

I see no benefit to this point at all. What of it?

I understand how videos and flipbooks work, and yes we use stills to create them, but the magic ingredient which you are ignoring is time (specifically non-zero intervals of time). We hold each frame for 1/24 seconds before advancing to the next frame. — Ryan O'Connor

Then why did you give the impression you didn't?

(I believe) Zeno's paradox was already informally solved by Aristotle. I'm just defending his view. And loosely speaking the view is simply that we start with videos, not stills. With videos we not only can capture motion but we can also pause the video to extract a still. With only stills, motion is not possible, as per Zeno. Zeno's paradox is important and seen as unresolved because the notion of stills being fundamental is deeply rooted in our beliefs. — Ryan O'Connor

I don't think we're having the same conversation anymore. But regarding your claim about video, I invite you to wave your arms in front of your webcam while recording, then play it back frame-by-frame. You'll see motion blur. I know this because I've seen it many times. In fact if you are making a video with the intention of capturing still frames you have to make sure to stay motionless for a few moments at a time to avoid motion blur.

The lockdowns, OTOH, are the greatest power-grab and policy flaw in the West maybe ever. The fallout from these lockdowns will be felt for decades hence. — synthesis

That's my belief. We save a life today and kill two tomorrow.

The WSJ just published an article the other day.

The Lockdowns Weren’t Worth It
There’s a reason no government has done a cost-benefit analysis: The policy would surely fail.

https://www.wsj.com/articles/the-lockdowns-werent-worth-it-11615485413?mod=djemalertNEWS

And

Did The Shutdowns Save Lives? A Year Later, Statistical Analysis Suggests Not
https://thefederalist.com/2021/03/12/did-the-shutdowns-save-lives-a-year-later-statistical-analysis-suggests-not/

What the past year has shown the ruling class is how easy it is to make docile sheep out of the populace. I don't think this is going to end well.

And who exactly is locked down and where? — tim wood

Disingenuous to the point of gaslighting. You deny there are lockdowns? Political overreach?

This is the point. When we use math to figure out things like instantaneous velocity, the volume of a supposed infinitely small tube, etc., — Metaphysician Undercover

This is exactly where you go off the rails. There is no "infinitely small tube." This is your ignorance speaking again.

it is implied that we know things about reality which we do not. This is a falsely supported certitude. — Metaphysician Undercover

Nobody is making any claims about reality. Gabriel's horn is a strictly mathematical example.

Or have I just created a false dilemma, a non-problem? — I don't get it

It's by design. I mentioned in another thread that I just happened to watch a video about Edward Bernays, Freud's American nephew, who was the father of public relations. During WWI he did war propaganda to get Americans to support the war effort. After the war, manufacturers were afraid that once Americans got everything they needed, they'd stop buying things and the economy would collapse.

Bernays used his uncle's idea that every human has unconscious desires, to get people to WANT things rather than NEED them. For example at the time, it was socially unacceptable for women to smoke cigarettes. He had the idea of putting into women's minds the idea that smoking was freedom and power. He got a bunch of models to smoke cigarettes in public with news photographers around. He branded cigarettes as "Freedom torches" and got women to start smoking.

Bernays was the first person to realize that you can get the public to buy a war using the exact same psychological techniques that you use to get women to smoke cigarettes.

It's ironic and depressing to see these old film reels of cute 1920's flappers smoking cigarettes, and realize most of them probably died of emphysema, lung cancer, and heart disease years ago. But that's how the American consumer society came into being. Industry figured out that you don't sell to people's needs. You sell to their subconscious desires. Whether it's war or cigarettes.

Today the name of Edward Bernays is long forgotten. But we live in the world he invented. You don't actually need the latest iPhone. But you WANT one, for reasons you're not even conscious of. Status, sexual desire, and so forth. Freud's psychological insights harnessed to American hucksterism.

It's not an accident that our entire economy depends on people buying crap they don't need. It's a deliberate plan. And the government is brilliant at selling wars to the people. We've been in Afghanistan for 20 years. Why? Well, it's for democracy and freedom or something. Ask anyone. What's the latest? Women's rights. If we leave, Afghan women will lose their rights.

This came out just last week. A crucial moment for women’s rights in Afghanistan

https://www.hrw.org/news/2020/03/05/crucial-moment-womens-rights-afghanistan

Is that really why we're there? Or is this just another propaganda psy-op? I can hear people firing up an angry post. WELL OF COURSE we support women's rights, are you some kind of misogynist? It's important for people to start to see the programming and manipulation we're all subject to. The very thoughts in our heads aren't ours, they're put their by master manipulators who've spent the last century perfecting the techniques invented by Bernays. To sell us wars, cigarettes, iPhones, masks (ooh fire up the angry tweets, he's an "anti-masker"), lockdowns. Some of it's real, a lot of it is perfected propaganda. The government and the media are very very good at manipulating public opinion. It's incumbent on all of us these days to try to step outside the process, even a little bit, to see how it works. The past year has been extremely instructive, in the fullness of time that will become more clear.

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

I think applying numbers to geometry is how we apply Godel's numbering to physics — Gregory

I don't think physics in its present form is amenable to methods of formal logic because there are no axioms for physics. Axiomatizing physics is Hilbert's sixth problem and according to Wiki it's still open. Even so I doubt that the axioms of physics, whatever they may eventually turn out to be, satisfy the premises of Gödel''s incompleteness theorems.

But of course you could Gödel-number anything, Moby Dick or the contents of this post. You assign numbers to the upper and lower-case English letters and punctuation symbols, and you apply Gödel numbering. So if 'abc" is your string, and a = 1, b = 2, c = 3 is your encoding of the symbols, then 'abc' is encoded as $2^1 \times 3^2 \times 5^3 = 2 \times 9 \times 125 = 2250$.

The idea is to use the unique factorization of integers into prime powers. To go backwards from 2250, we note that it's $2^1 \times 3^2 \times 5^3$ and read off the exponents, 1, 2, 3 to get 'abc'. You could do this with any piece of text.

As you can see, if you believe that the positive integers exist (whatever existence means for you) then every finite-length document that could ever be written, already exists. It's already encoded as some positive integer. LIkewise if you pixellate a painting finely enough so that the pixellated version is indistinguishable from the original (to the naked eye, say) and encode its color and texture values, you can Gödel-number all possible paintings. Likewise songs, etc.

Or as the Pythagoreans said: All is number!

Yes, because that is the convention, use some math, and figure out the "instantaneous velocity", just like the convention is to place a zero limit on the example of the op. But what these conventions really represent may not be what one would expect from the terms of usage. — Metaphysician Undercover

A car whose speedometer reads 40mph is going 40mph at that moment even though that's a mechanical approximation. But as I say I'll concede you've moved me off my certainty and I've run out of talking points. After all we don't know the ultimate nature of reality so who's to say if the notion of instantaneous velocity really makes sense. Based on that I'll concede the point.

That's why velocity is always an average, requiring at least two temporal points. Duration is derived, just like distance is. To infer an instantaneous velocity requires a second derivation. — Metaphysician Undercover

A moving body has an instantaneous velocity, even though our formalism requires two temporally separated measurements. But, I'm willing to concede that you've either made your point or at the very least caused me to doubt mine.

Why does a segment with a length of finite digits change into a length multiplied by pi (pi×2×r) when the segment is made into a circle? The circumference will have digits going to infinity while as a segment it did not? This must be readily explained in mathematics but I don't remember ever seeing an explanation on it — Gregory

Just an artifact of the decimal representation. Doesn't mean anything. Roman numerals had drawbacks, decimal representation has drawbacks. Every notation has some advantages and some drawbacks.

As to why a circle's circumference and radius are incommensurable, I think that's one of God's little jokes. God in Einstein's sense. Not necessarily religious, but a stand-in for all the ineffable mysteries of the world. With a sense of humor thrown in.

Your guess is as good as mine. There's no actual reason. But the diagonal of a square seems like an even simpler example. One unit to the right, one unit up, and the distance between your start and end points is incommensurable with 1. No reason at all, just a shocking surprise.

How can anyone deny the existence of the length of the diagonal? That's the part I don't get.

Nope. They can't see past the headlines. Not ever. — Book273

A year of hysterical media propaganda has really messed with people's minds.

I watched a Youtube video last night about Edward Bernays, the father of public relations. He was Freud's American nephew. He was the first person to realize that you can sell the public a war using the same techniques you use to get women to start smoking cigarettes ("Freedom torches!"). His name is forgotten but we live in the world he invented.

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

Most deaths are perfectly normal and not tragic in the least. — synthesis

They're tragic to the deceased's friends and loved ones. I'm willing to stipulate that the covid deaths are bad but so are the collateral deaths and misery we're inflicting with the endless politicized lockdowns.

Please explain how every death is a tragedy. Then explain how deaths are bad. I don't follow either of these assumptions. It's like rain is bad and when rivers flow into the ocean it is a tragedy. Natural, normal and predictable linear systems, somehow bad and tragic? — Book273

Was it Stalin who said a single death is a tragedy, a million deaths is a statistic? He'd know, he killed more people than Hitler but he was FDR's good buddy so we let Stalin have half of Europe after the war. Patton was right, we should have kept on going.

Anyway, "every death is a tragedy" is something you say when you're trying to get people to see that there is a balance between avoiding a death today only to create two deaths tomorrow, and they call you names because you're "heartless" and "an uncaring prick" and so forth. But I do believe every death is a tragedy, yet the two we cause tomorrow by avoiding one today need to be considered.

Imagine a dark room and a quantum sensor — Ryan O'Connor

So you're no longer talking about cameras but rather quantum sensors? It would be better if you dropped these labored analogies and just made your point some other way. Are you saying photons use quantum tunneling to show up on the sensor without the shutter being open? This is such an unproductive tangent to the discussion. To record an image on a photographic medium you have to expose the medium over a period of time. You're stepping all over your own point, we're not talking about cameras we're talking about something else and this isn't making sense.

I believe that's a false equality. — Ryan O'Connor

Oh boy my mentions have piled up tonight. I wanted to respond to this before diving back into the maw of the slavering mob I triggered by daring to express a political opinion they don't like. But never mind all that.

The correct statement is "the potentially infinite process defined by 0.333... converges to the number 1/3" not "the number 0.333... equals the number 1/3". — Ryan O'Connor

Before going on @Metaphysician Undercover pointed out a distinction we need to nail down. Please respond clearly to this question. Are you talking about

* Mathematics? or

* Some kind of notion of reality that goes beyond math?

If the former, you're just wrong. 1/3 = .3333... because the right hand side is just the sum of the infinite series 3/10 + 3/100 + 3/1000 + ... which equals 1/3 since it's a geometric series as taught in freshman calculus. It does you no good to demonstrate ignorance of the theory of limits. The sum is defined as exactly 1/3, not "approaching 1/3" or "infinitesimally less than 1/3" or any similar confused location that calculus students often have after slogging through the course. Mathematically you're wrong as a matter of fact.

On the other hand if the latter, I have no idea what you mean, because 1/3 = .333... as a matter of formal mathematics. I can prove it directly from the axioms of ZF set theory. There is no question about it. It's as certain as saying that a certain chess position follows from the rules of the game. You'd be better off self-studying real analysis than wasting your time telling me about your mathematical misunderstandings. And if you think it means something reality, you're likewise wasting your breath because I have no interest. I'm doing math, not metaphysics; and frankly I'm not sure 1/3 OR .333... OR the number 47 have any metaphysical meaning at all. That's a completely different subject.

Decimal notation is flawed in that it cannot be used to precisely represent some rational numbers, like 1/3. If we want a number system which can give a precise notation for any rational number, we should use Stern-Brocot strings, where 1/3 = LL. — Ryan O'Connor

I don't understand why you like one infinite representation rather than another, but you are riding a hobby horse and making no rhetorical points with me at all. You're wrong on the math and confused on the metaphysics.

If photographs can't capture motion but videos can, why not conclude that motion happens in the videos? The reason why we are reluctant to come to this conclusion is because we reject the notion of videos being fundamental. — Ryan O'Connor

No not at all. First, video is nothing more than a series of stills, whether analog or digital frames. Have you ever seen a flip book? We see the illusion of motion from a sequence of still images because our eye-brain system retains a little afterimage for a fraction of a second. That's how movies work, I'm certain you must know that. Back in the old days I believe flip books were a common medium for the pr0n of the day but I found a really nice G-rated contemporary flip book artist. This video is worth checking out for its own sake and makes this point dramatically. Video is nothing more than a rapid sequence of stills. It depends on a quirk of your eye-brain system.

https://www.youtube.com/watch?v=ntD2qiGx-DY

Secondly, how about still photos? If you ever had a DSLR or film SLR you know that one of the important controls is the shutter speed. You hold the shutter open for a period of time, usually a fraction of a second, and during that time interval photons come in and hit the film or digital sensor. If an object is moving side to side in front of you, you can always determine its velocity by setting a long enough shutter speed that you get some motion blur; then you can work backwards from the blur to determine the velocity. You know, the same reason your low-light photos taken with your automatic camera are blurry. The camera compensates for the low light by choosing a slower shutter speed, and your shaky hands cause motion blur.

So still photos actually take time, and videos are just a sequence of stills.

We want points (photographs) — Ryan O'Connor

Why are you saying this? I assume you must know it's wrong, no mechanical device is capable of exposing a light-sensitive medium for a true instant. Are you speaking metaphorically? If you set your hypothetical camera to an instantaneous shutter speed no photons could get in and the image would be blank.

to be fundamental and continua (videos) to be composite and as long as we hold this view we will not find a satisfactory resolution to Zeno's paradoxes. — Ryan O'Connor

We're not going to solve Zeno's paradoxes here. Better you should try to understand some math, in particular the sum of a geometric series.

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

If you flip things upside down and see continua as fundamental and points as emergent, then everything makes perfect sense. There's no problem with pausing a video to produce a static image. — Ryan O'Connor

Utter nonsense. If you put your webcam on yourself, record at 30 frames per second, and move around, then play it back frame-by-frame, you will most definitely see motion blur in each frame. Unless you are speaking metaphorically about an idealized camera, you are just wrong on the technology. And an idealized camera with infinitesimal shutter speed could not transmit any photons to the light-sensitive medium, so it wouldn't work.

It is clear that you appreciate the profoundness of Zeno's Paradox. Zeno presented these paradoxes in response to the criticisms from the 'one from many' camp calling his views ridiculous. Why not consider the 'many from one' view that he supported? He was wayyy ahead of his time so his view did seem to have problems of their own...but in light of modern advancements in physics his view no longer seems crazy. — Ryan O'Connor

We're not going to resolve those ancient issues here.

Don't stop here, you may just be on your way to becoming a crank! With this admission you have placed yourself on a slippery slope. Instantaneous velocity is no different from the tangent of a function at a point. Do you accept that the derivative corresponds to a limiting process of secants rather than the output of a completed infinite process (i.e. tangent at a point)? — Ryan O'Connor

What? The tangent line IS defined as the limit of the secant (for a function from the reals to the reals). That's how they motivate it. But in fact that is the DEFINITION of the tangent line. Without the definition, we don't even know what a tangent line is.

Only if you consider 0/0 a valid velocity. — Ryan O'Connor

You're confusing the formalism with reality.

"I went down to the demonstration ... to get my fair share of abuse ..."

I'll close for the evening by linking and quoting a nice article by Jonathan Sumption, writing in The Telegraph.

https://archive.is/WDOBR

Liberal democracy will be the biggest casualty of this pandemic
The state's unprecedented overreach has fundamentally altered the unwritten conventions that underpin our political system

What makes us a free society is that, although the state has vast powers, there are conventional limits on what it can do with them. The limits are conventional because they do not depend on our laws but on our attitudes. There are islands of human life which are our own, a personal space into which the state should not intrude without some altogether exceptional justification.
Liberal democracy breaks down when frightened majorities demand mass coercion of their fellow citizens, and call for our personal spaces to be invaded. These demands are invariably based on what people conceive to be the public good. They all assert that despotism is in the public interest.

and ...

I do not doubt that there are extreme situations in which oppressive controls over our daily lives may be necessary and justified: an imminent threat of invasion, for example, or a violent general insurrection. Some health crises may qualify, such as a major epidemic of smallpox (case mortality about 30 per cent) or Ebola (about 50 per cent).
Covid-19 is serious, but it is not in that category or even close. It is well within the range of perils which we have always had to live with, and always will. According to government figures, more than 99 per cent of people who get Covid survive. The great majority will not even get seriously ill. The average age at which people die of Covid-19 is 82, which is close to the average age at which people die anyway.

Much more in the article. Instead of venting your spleen at the likes of me, take a deep breath and give this article a read.

https://archive.is/WDOBR

You take a snapshot of a moving car. You look at the photo and ask, "How fast was it going?" — jgill

You know, this is more tricky than it looks. Suppose you have a long exposure time. Then you'll see a blurred image, and you can work backwards to determine the velocity. Photographs are not instantaneous. The shutter stays open for a period of time, usually a fraction of a second. During that time the film or digital sensor collects photons. So there's an element of time involved even in a photo. If the object is moving slowly relative to the shutter speed you won't see blur, but in theory the blur is always there. If I can choose the shutter speed I can always tell you how fast the object was moving by analyzing the blur.

@Ryan same point to you. In fact your earlier point is correct, any measurement is taken over time. There's no difference between photo and video. Video after all is just a collection of still images, either analog or digital frames. And a single photo is taken over a period of time, namely the shutter speed.

:rofl: — Banno

Grrrr snarl rowrrorrwrnrrrowr

But fentanyl, oxycodone, heroine, meth, other drugs, and alcohol have been a leading cause of death in the affected demographic for 2 or 3 years, at least -- haven't they? — Bitter Crank

I believe the numbers are up this year. A lot of statistical sifting will happen over the next couple of years and maybe people will get more perspective. But you know flu deaths are way down this year. Why is that? Well masks and social distancing and lockdowns, maybe. And maybe a lot of flu deaths were recorded as covid. The diseases look similar and you can make anyone have a positive covid test by running enough PCR cycles.

I would not want to minimize the consequences of the lockdown. — Bitter Crank

Careful, you're going to end up in the same barrel of opprobrium that I stepped into. Whatever you do, don't be thoughtful. Hey seriously I'm feeling a little bruised. Thanks for the rationality.

While I am an old guy and don't get around much any more (every day is a sort of lockdown), — Bitter Crank

Me too, the funny thing is that my own personal lifestyle barely changed this past year. How pathetic is that!

that's not true of younger people. Some people think the shutdown in Minnesota contributed to the ferocity of the riots last may that did so much damage, and the crime wave that has followed. I'm not sure about that, but it seems plausible. I'm sure the lockdown has been quite emotionally distressing to children and youth. — Bitter Crank

You tell the kids they can't go to the bar but they can go to the riot. So you get riots. And peaceful protests that turn into riots once the Antifa maniacs (all middle-class white kids) start burning things down.

The lockdown was an economic disaster for service workers in closed businesses -- absolutely no doubt about that. Use of food shelves has been very high. Homelessness has increased too. — Bitter Crank

Yes but you see coastal liberals don't give a shit about working people. They used to, the old Wobblies and the labor movement was supported by leftists. Today leftists don't care at all about working people. Bunch of deplorable racists. Part of the corruption of liberals I rail about. Frosts my butt because I used to be a liberal. Still am. It's the liberals who changed. I care about the working people destroyed by the lockdowns. And for this I get called a "selfish dick." Thanks @@Banno, you should know better and you should be ashamed of what's happened to liberalism. Liberals used to care about working people. That was a long time ago.

Still, 530,000 dead from Covid-19 in the US is unlikely to be matched by deaths from domestic turmoil caused by the lockdown. 2.6 million Covid deaths world-wide is more than a blip on the radar, but it's a fraction of world deaths from all causes. — Bitter Crank

Yes, I don't discount or deny the deaths. It DOES happen to be the case that a lot of those people died WITH covid and not FROM it, and that global net excess deaths aren't going to turn out nearly as bad as people think, because for the most part only old people died of covid. Yes there's anecdotal evidence of young deaths, but for the most part it's people who were going to die anyway of something else.

By contrast, in the 1918 Influenza Epidemic, about 1/3 of the world's population became infected with influenza and around 50 million died -- that at a time when world population was significantly smaller than now -- below 2B. 50 million dead from influenza was close to a doubling of total deaths world wide. — Bitter Crank

My point exactly. Thanks so much. I really appreciate your response. I took more personal abuse than I was expecting for the fundamentally obvious points I was making. Percentage-wise in terms of fataility rates, total deaths, and excess deaths, all of that versus the effects of the lockdowns, in the end I stand by my initial remarks and wish some of my detractors would put some thought into the matter.

I didn't look at your list of links -- too late just now to do that, bed time coming up. But I still think the strategic business closures, social distancing, mask wearing, and avoidance of group gatherings helped — Bitter Crank

We'll see! You can find anecdotal evidence that masking and lockdowns function more as a means of social signaling than health preservation. We'll have to way for the politicized statistics to roll in over the next couple of years.

Thanks much for your post.

My rough impression is that professionals in the field of philosophy of mathematics usually do know about mathematics. Which philosophers in, say, the last 85 years do you have in mind? — GrandMinnow

Mostly the ones here. The famous philosophers of math know a lot of math, like Putnam and Quine and so forth. I may have overstepped a bit. Having just stuck my contrary toe in a political thread I think I've had enough for tonight. You know when you say something contrary to the dominant narrative, people don't just respond rationally. They come with insults and non sequiturs. It's like the 1950's all over again and I just came out as a Commie.

They are selfish dicks. — Banno

If you can dial down the insults for a moment, is it selfish of me to care about the locked down kids killing themselves because the can't go to school? The fentanyl deaths even right here in my little town? Not to mention the horrendous effects on the third world due to the disruptions in the global supply chain. When food prices go up, I pay a little more at the grocery. Impoverished peasants die.

Does caring about these things, or calling attention to them, make me a selfish dick? I'm asking you. Can't you see past the hysterical propaganda to the far more complex and nuanced reality underneath?

Bullshit. They are selfish dicks. — Banno

Bullshit bullshit bullshit. People who think they know better but don't are a great source of evil in the world. You know that liberal condescension is the greatest knee on the neck of black people in this country for the last 60 years. Read the Moynahan report. He pretty much got cancelled for writing it and never mentioned it again.

You don't know what you don't know, friend. Thoughtless do-gooders have killed more people than the actually evil ones.

https://en.wikipedia.org/wiki/The_Negro_Family:_The_Case_For_National_Action

https://www.blackpast.org/african-american-history/moynihan-report-1965/

Ethics involves care for others; that seems to be beyond their comprehension. — Banno

That's a really nasty remark with little or no thought behind it. Don't you have compassion for the victims of the lockdown? It's a lot like environmentalism. Every time you reduce the parts-per-million of pollutants in the air, the liberals in NY and LA are happy. And a few hundred thousand third-worlders die of malnutrition secondary to rising energy costs. A lot of people hide behind compassion out of an excess of arrogant thoughtlessness.

The problem with this perspective is that "mathematical existence" means something completely different than "existence" in the philosophical sense. — Metaphysician Undercover

I agree.

The op does not ask about "mathematical existence", it asks about "existence". — Metaphysician Undercover

I believe I asked the OP what they meant by existence and don't believe I've gotten an answer.

If it asked about the mathematical existence of irrational numbers there would be nothing to discuss. Clearly irrational numbers are used by mathematicians therefore they have mathematical existence. — Metaphysician Undercover

Ok then you are in agreement with my point. I only speak of mathematical existence. But why the square root of 2? How about the number 3? That has no more claim on existence than sqrt(2). That's why the OP is confused. They think 3 exists but not sqrt(2). I think they both have mathematical existence, and as far as "existence existence," I'd like to see a coherent argument one way or the other. I take no position at all. Clearly numbers don't have the same claim to existence as rocks or fish.

The op is asking a philosophical question about the existence of certain mathematical objects, not whether those mathematical objects have mathematical existence. — Metaphysician Undercover

This thread hasn't even begun to touch on the subtleties of that subject. I've seen no decent arguments one way or the other. And if that's what the OP really cared about, they'd have asked if 3 exists. Once you bring in sqrt(2) you are talking about mathematical existence.

That would be self-evident. So mathematicians who hardly know anything about existence, yet think they do because they know something about mathematical existence really seem to have very little to say about the philosophical question of whether certain mathematical objects which obviously have mathematical existence, have existence. — Metaphysician Undercover

It's "above their pay grade" as Obama would have said. So make an argument. Do you think 3 exists? Of course the positive integers have a pretty good claim on existence because we can so easily instantiate the smaller ones. So how about $2^{\text{googolplex}}$? That's a finite positive integer that could in theory be instantiated with rocks or atoms, but there aren't that many distinct physical objects in the multiverse. So make an argument, say something interesting about this. Forget sqrt(2). Do you think that extremely large finite positive integers exist?

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

There are many non-fatal consequences of these mental health issues, such as increased self-harm by children. — tim wood

Well the hell with the kids then. They ain't dead so eff 'em.

So far you've got nothing, and it's more than a little disturbing that you think you do. — tim wood

I stand by what I wrote and expect to be vindicated by history once the hysteria passes. Compared to the Spanish flu of 1918, covid has been very minor in terms of excess deaths. The death rate is far far lower than we were initially told. There has been a sickening lack of thoughtfulness in the actions and public pronouncements of politicians and public health officials. I expect people to understand this point of view more over the next few years as people being to put this all into perspective. Right now I'm standing in the middle of a witch burning with a bucket of water. It's futile but the viewpoint needs to be expressed regardless. More important now, when it's unpopular, than a few years from now when it will be obvious in retrospect.

The overreaction and politicization have been horrible. Consider if nothing else that one week anti-mask demonstrations were evil, and the very next week BLM riots mostly peaceful demonstrations were just oh-so-safe. One week we get propaganda photos of nurses standing in front of cars to confront anti-maskers; the very next week, photos of nurses protesting police brutality. A thoughtful and independent person like myself knows that a virus doesn't discriminate based on politics. Can't you recognize politicized media coverage when it's right in front of you?

stick to math — tim wood

We live in an age of tremendous political conformity. Step out of line and get cancelled. I wonder why so many are ok with it. It's worse than the 1950's. Our only hope is to remember that the children of the 50's turned into the hippies. The 2030's are going to be wild.

Fishfry is a nice guy, but the quoted statement is BS. — Bitter Crank

Please see my response to @tim wood above. I stand by my claim.

Do people have any idea of the effects of the lockdown on substance abuse, domestic violence, child suicides? Some more links on the latter. You can Google dozens of more stories like this. It's shameful that so many well-meaning people are hypnotized into ignorance by the mainstream hysteria.

We're also starting to see statistical evidence that lockdowns weren't all that effective. For example Florida and California had similar outcomes even though Cali was locked down tight and Florida much more loose. You'll see more information coming out along these lines in the coming months.

Finally as I said in my previous post, excess global deaths aren't much greater for 2020 than they otherwise would have been. When an 80 year old with cancer and pneumonia dies of (or with) covid, they would have died anyway. And a large plurality (if not outright majority) of covid deaths were among old people with multiple comorbidities. Every death is a tragedy, but intelligent and thoughtful people need to be able to hold two ideas in their minds: One, that the deaths are bad; and two, that in many cases they have been politicized.

Toxic lockdown' sees huge rise in babies harmed or killed". This is from that well-known conspiracy theory site, the BBC.
https://www.bbc.com/news/education-54827702

"Child Suicides Rising During Lockdown" from WebMD. Another notorious site from covid deniers.
https://www.webmd.com/lung/news/20210210/child-suicides-rising-during-lockdown

"Child Psychiatrists Warn That The Pandemic May Be Driving Up Kids' Suicide Risk" from NPR. Oh NPR, they're the worst. The Devil's very playground.
https://www.npr.org/sections/health-shots/2021/02/02/962060105/child-psychiatrists-warn-that-the-pandemic-may-be-driving-up-kids-suicide-risk

"Child suicides are rising during lockdown: Watch for the warning signs"
https://medicalxpress.com/news/2021-02-child-suicides-lockdown.html\

"Escalating Suicide Rates Among School Children During COVID-19 Pandemic and Lockdown Period: An Alarming Psychosocial Issue"
https://journals.sagepub.com/doi/full/10.1177/0253717620982514

Fishfry is a nice guy — Bitter Crank

Aw shucks.

Can you elaborate on this? Interested on how lockdowns, in themselves, will kill more people. — Trips

Please see the links in this post and my previous one. You can easily find many more by typing "lockdown deaths" and "child suicide lockdowns" and similar phrases into the search engine of your choice. And thank you for simply asking for background and supporting evidence, rather than parroting mindless hysteria and false accusatios like certain people I could name, @tim wood.

But hey, that Covid is nothing, barely even real. So what if in one year it has killed a lot more Americans than were American soldiers killed in all of WWII - but that's probably fake news, right, — tim wood

This is exactly the kind of mindless response I expected. I pulled a few links in support of the point I made, which you can read or not. The links reference reports by the likes of the UN and UNICEF and other reputable sources of information. I say again: In the end, the lockdowns will kill more people than the virus. I stand by this claim. Any fair minded person can see that I did not say the things you imputed to me. You can also look up the statistics on excess global deaths for 2020, which are barely above normal.

https://unglobalcompact.org/take-action/20th-anniversary-campaign/covid-related%20hunger-could-kill-more-people-than-the-virus

https://www.internationalaffairs.org.au/australianoutlook/lockdowns-could-kill-more-people-than-covid-19/

https://fortune.com/2021/01/06/covid-pandemic-recession-unemployment-mortality-rate-increase/

https://www.axios.com/navarro-coronavirus-lockdown-ef2a1335-661b-4f8b-a3a4-79af244f9bbf.html

https://bylinetimes.com/2021/01/12/do-lockdowns-kill-more-people-than-they-save-how-quickly-can-the-economy-bounce-back/

https://www.telegraph.co.uk/global-health/science-and-disease/unicef-warns-lockdown-could-kill-covid-19-model-predicts-12/

https://timesofindia.indiatimes.com/blogs/seeing-the-invisible/estimating-the-true-magnitude-of-the-pandemic-and-lockdown-deaths-part-1/

https://economictimes.indiatimes.com/news/company/corporate-trends/lengthy-lockdown-will-kill-more-people-than-covid-murthy/articleshow/75459491.cms?from=mdr

It is far from clear to me that lockdowns to prevent a virus from spreading are ethically justified. — Bartricks

In the end the lockdowns will kill far more people than the virus ever did. The entire episode's been an exercise in mass hysteria and social control. A preview of what's coming, now that the powers that be have seen how compliant and easily controlled we are.

I am not the one using those terms, but rather my university professor. — Amalac

I understand that, and I'm objecting to the usage.

But you are right in that it probably doesn't make sense when taken literally. — Amalac

Then we're in agreement. And the reason I mention it is that it's all too common for people to use "infinite" as a substitute for "really really big, but finite." And it's confusing and wrong to do that. Physicists do it a lot, even big-name professional physicists. I saw Leonard Susskind being interviewed once about the multiverse, and he was asked whether there are infinitely many universes. He answered, "There are 10 to the 500 types of universes". But that's a perfectly finite number. And I read one of his papers on infinity once and he made the same error, confusing a large finite number with infinity. And he's a big name in physics.

Perhaps he was trying to say: It was far more likely for the universe not to have existed, since such a scenario is far simpler than the scenario in which the actual world exists, for the reasons given before.

What would be your response to that then? — Amalac

That this is exactly how he should have phrased it!

Why do you think its incoherent and meaningless? — Amalac

What does it mean? Infinity has particular technical meanings in math. If you're using it as a synonym for "lots and lots" or "really really big but still finite," you're making an error that leads to weak and confused thinking.

They would not argue that a universe without a rock or without the sun or the milky way is infinitely simpler, they would argue: the less things there are in it, the simpler the scenario is. And it reaches its simplest state when there is absolutely nothing in it, where infinitely many things don't exist (or at least where a huge amount of things don't exist). — Amalac

The phrase "infinitely more likely" is incoherent. It's meaningless. And worse, it obfuscates thought. It's a phrase that literally short-circuits precise thinking. It's wrong at every level.

I agree. By treating rationals and irrationals both as the same type of object (i.e. numbers) we blur the line between the output of a finite algorithm and the output of a potentially infinite algorithm. — Ryan O'Connor

What do you make of 1/3 = .333...? Can't you distinguish between a number and one of its representations that you don't happen to like? After all 1/3 is just a shorthand for the grade school division algorithm for 3 divided into 1.

Why would you think that someone who has not studied existence would know as much about existence as someone who has studied existence? — Metaphysician Undercover

Because there are SOME subjects in which more study implies more knowledge; and others where it doesn't.

If you study more math you know more about math than someone who doesn't study math. Medicine, physics, and history are in this category.

But take, say, baseball. A non-athlete spends his life studying the game. Reads books on strategy and tactics, knows all the statistics, can name all the players on the 1928 Philadelphia Athletics and their batting averages. Another person knows nothing of the history of the game but has been playing all their life and has been toiling in the minor leagues for years (think Bull Durham). Who knows more about the game? I would say the practitioner and not the student.

Existence is the same. If someone's been existing for a few decades they know as much about existence than a philosopher. The philosopher knows the history of what great thinkers have written about the subject. But philosophy does not confer actual knowledge of its subject; only knowledge of what others have said.

Philosophers don't necessarily lead better lives than others, nor are they more moral, and they most definitely don't know any more about existence than the general public.

In particular, a philosopher who knows hardly anything about mathematics is in no position whatsoever to comment on mathematical existence. Many philosophers of mathematics are in this position. They simply don't know enough math to comment intelligently on the subject of mathematical existence.

Like I said in my OP, I think the reason he, like Martin Gardner, says that is beacuse of an argument like this: — Amalac

I don't think your post addressed what I said. A universe without a particular rock is a little bit simpler than the one with it. But it's not "infinitely" simpler. It's the vague and meaningless use of "infinitely" that I'm objecting to.

The point being, that you cannot take the arrow at a particular moment in time. — Metaphysician Undercover

I'm mostly in agreement with you on this point, as reading the rest of my post would have indicated.

However, just because we apply delineation through our act of retrograde analysis, and create a mathematical notion of temporality, that doesn't mean that the thing did not have a momentum at a particular instant. It's only a question of accuracy. — emancipate

I'm confused by your post. You make the correct point that the math is just a model of reality, not reality itself. Then you say that the thing DOES have a momentum at a particular instant. Which is what the mathematical model says.