Sometimes very active discussions about peripheral issues overwhelm a thread, so this is a permanent home for those conversations.
I’ve opened a new “Sandbox” thread as a post as the new “ignore commenter” plug-in only works on threads started as posts.
I wonder what he’s looking at when he sees what he wrote.
Historically, conservatism has been a valid and important political force. Liberals want change to happen rapidly, and conservatives have seen the dangers of changes too rapid to allow for adjustment and settling in. As for the politics, conservatives quite rationally have wanted smaller government, lower taxes, less regulation, more individual freedom (but with serious consequences for abusing that freedom).
I see the reluctance toward government providing social services as fairly closely tied to the fact that the US is a lot more religious in general than Europe. From the religious viewpoint, too much of what people do with their individual freedom is sinful. There’s also a lot of bigotry and xenophobia becoming more evident because of efforts to address it. So we see a widening gap between political conservatism and social conservatism, and today we have politicians fanning the flames of culture wars for political gain.
Very few countries would enjoy having their history held up to a microscope.
During the Vietnam war, Canada was held up as a paragon of sanity and virtue.
But they probably aren’t proud of some stuff they did in WWI.
Or some of their pioneers in eugenics.
I almost have to laugh when I read people on all sides weep and wail about how bad it is now.
My parents survived WWI, the 1918 flu, the depression (just as they were seeking their first jobs), WWII, Korea. And they were privileged. Less fortunate Americans endured slavery, Jim Crow, internment. Cambodia endured a genocide.
When I say things have gotten better over time, I mean nothing recent has really been as destructive as these.
One thing about covid. Assuming the worst reading of statistics, there were 20 million excess deaths. That’s 0.3 percent of the world population, and predominantly old people.
The 1918 flu killed one percent of the world population. And it did not discriminate by age.
petrushka,
Yeah, we’ve covered this ground before, although you were between 15-fold and 150-fold off (you quoted 0.02%, and then converted that to 2 per 100,000!! Math not your strong suit, evidently) when you last made this comparison. The comparison with Chicxulub still applies.
Looking at your list, I do not see how anything has gone better. More likely that we have become desensitised to how bad things are.
The current quarter of a century has seen Afghanistan and Iraq wars, SARS pandemic 2003, Indian ocean tsunami 2004, recurrent avian flu outbreaks, 2010 volcano eruption on Iceland that closed European airspace, ISIS and Syrian refugee crisis, Great Recession, ebola, covid, and Ukraine war along with Ukraine refugee crisis. Human trafficking (which is what slave trade looks like nowadays) is on the rise (roughly proportionate to refugee crises). And of course, W and Trump, the worst presidents of USA ever also happened within this quarter of century. And I may be forgetting some important events.
Do you care about statistics on mass shootings perhaps? USA always looked very bad compared to the rest of the world on this one and it keeps worsening. But if you do not care, then this proves my point: You have become densitised.
I don’t know whether the human condition considered globally has improved all that much in the last century, but I think on balance it has according to a few meaningful metrics like lifespan and some hazy notions of standard of living. Yes, as you point out, there always have been and always will be diseases, catastrophes, wars, and various evils.
I think my main concern is that people have been living beyond their means in terms of global carrying capacity, and I suspect the bills will be unpayable in a generation or two. Populations that overbreed eventually implode, and when the human population implodes, the survivors will inherit an impoverished world.
DNA_Jock,
I’m not sure how I typed all that. My intention was to say covid has been about one third as deadly as the 1918 flu, per capita.
And considerably less deadly in terms of years of life lost. But since I am bad at math, I’ll wait for someone else to do that calculation.
I’d take that bet, but it would be moot. Even optimistically, I’ll be dead in two decades.
I suspect in a decade, the big crisis will be the population implosion. There are actual spooky people in high places talking about population reduction, but I doubt if it requires a conspiracy. It’s happening in every developed country.
Looks like you are worried more about overpopulation than about ecology. I personally am worried more about ecology, to do with the wasteful way of life rather than overpopulation.
Growth rate of population is very uneven. Hardly any Western developed nation has a natural growth rate in population. The overpopulation occurs in the world’s poorest areas, often places suffering from famine and war.
My theory is that humans as a species breed like rats: The worse the conditions are, the more breeding there is in order to ensure the preservation of the species. Urbanisation tends to put a stop on breeding, particularly when the living conditions become tolerable in individualist terms (a multi-room apartment per every family), while communal lifestyle (multiple families per apartment) still keep the breeding going.
If overpopulation is your worry, the solution is to give everybody a small house and guarantee them a basic income so they have little reason to leave the house. Problem solved. In fact, has been solved across the Western developed nations.
I don’t see these things as being separate and distinct. Ecological problems are the result of overpopulation. Yes, Western developed nations have experienced declining birthrates, but remain WAY over-represented among the world’s polluters and resource consumers. If you could somehow cause everyone to vanish except those in nations whose birth and death rates balanced, the world would STILL not have enough resources to maintain the remaining people indefinitely at current per capita consumption rates.
Now, a long-term equilibrium might be reachable while still retaining a decent living standard among those remaining nations, but nonetheless this would require some serious modification of what we’d consider a good standard. I’d like to know the effective global footprint of what would be considered minimally adequate in lots of areas, from transportation (of goods as well as people) to space exploration to product packaging and the list goes on and on. How much power do I really need for my climate control, my appliances, my vehicles? How much fresh water do I consume that I could do without? Do I need a lawn and the equipment to maintain it? How much efficiency to we gain with centralized employment and long commutes?
How much of the stuff I have surrounded myself with is “waste”? What is the total footprint of the internet, when we include the infrastructure of all the cabling, the access equipment, the computers, the power to run it all? Would we experience a global power and resource savings by eliminating it all? Would life be perfectly acceptable without any of it?
Big families are perhaps beneficial in societies that survive by manual farming methods, but it’s not the populations doing the overbreeding who are responsible for global warming. If Western standards of living are considered the desirable target, what global population enjoying those standard would be the maximum that could be maintained at a population equilibrium?
I don’t see it this way at all. In my opinion it is very much up to lifestyle, way of life, or the way “civilisation” operates.
Ancient Rome at its high point lived far beyond its means, importing grain from Egypt and wood from Germany. But at its low point, prior to it becoming the ancient Rome we know, it sustained itself on Italian grain and wood just fine. For sure there was a difference between population, but I believe the lifestyle was the more significant difference. The way a person lives, lavish versus austere, should make more of a difference than the mere fact that the person exists.
I’m from countryside myself and back in the days when I was young the countryside was very lively, plenty of children like myself when I grew up. At the same time we had forests and clean water and we recycled everything by ourselves. By now the countryside has died out compared to those days, so nature should be taking over, grass should be growing on the roads, trees through the roofs of abandoned houses etc, right? Wrong. Modern agriculture, forestry and other industries are driving through, cutting down and digging up every inch of land. The population (also nationwide where I happen to live) has decreased, but the ecological footprint has increased.
The current greenie call to people to change their lifestyle individually is totally misguided. The change for the worse has been happening on industrial scale globally. It’s due to the values the capitalist society has, get rich quick, buy more shiny stuff and nothing else matters. So to change it one needs to reorient the profit incentives of industries and corporations first and then the individuals will necessarily fall in line later. If you want people to stop buying crap, just stop selling it and stop producing it.
But it will never happen. City people will never give up their urban lifestyle. Modern ecological urbanists believe, wrongly, that urban lifestyle is less wasteful than rural lifestyle.
In my opinion a huge socially motivating factor to preserve ecological resources like wood, food, and water is direct knowledge of how the resources come about. In the countryside when you have your own well, that’s where the water is coming from, so you take care of it. When you know the forest where your wood comes from, you take care of it. When you raise your own food, you have the connection with it and you chew with very definite appreciation. And you will generate as little permanent waste as possible and not mix it with your wood, food and water. Naturally, if wood, food and water are your only resources, then there will be no permanent waste whatsoever.
In the city this connection is necessarily lost as people specialise or become civilised. They see water running, but they do not know where it comes from. They can flush away their waste, but they do not see where it goes. This lack of experience is so debilitating that city people never understand the weight of this point. Unfortunately, they, the city people, are the ecological tipping point in every nation and as long as they refuse to change, there will be no change. Therefore ecology has no chance. What I have seen in the ecological movement for the past century is silly and ignorant city people posturing.
The population implosion is inevitable. For the city people it will be the end of the world. For the deep countryside it will be a relief.
An observation: Have you noticed that when you google a prominent person X who also happens to be physically attractive, invariably some of the autosuggestions are of the form ‘X married’ and ‘X husband’ or ‘X wife’?
It’s understandable for celebrities, who often owe their success at least partially to their looks. But when it’s for a scientist or an academic or some other public intellectual, it’s funny.
I was reminded of this when I googled Sarah Haider, the founder of Ex-Muslims of North America:
The autosuggestions are apparently ordered according to how frequently they have been searched in the past, and the order reveals a lot. For Sarah Haider, ‘husband’ and ‘married’ were near the top of the list, and ‘education’ was toward the bottom.
One thing about which I’m certain is that people, in the aggregate, change their behavior when incentives Change.
When infant and child mortality exceeded 50 percent, people had, or tried to have, more children. That incentive is gone in the developed world, and diminished everywhere else.
Before welfare systems, children were expected to care for parents when the parents became sick, disabled, or elderly. That expectation is gone or drastically diminished.
When nations worried about population downtrends, they incentivized parenthood. Now the consensus among pundits and potentates is we need population decline. (Strictly speaking, nations seem to favor a declining birth rate, but increased immigration, because population decline has tax and budget implications.)
It does not surprise me that many upscale governments are producing policies and propaganda that encourage childlessness. In my lifetime the prevailing social attitudes have moved from scorn and pity for the childless, to scorn for parents.
I would find it amusing to know the birth rate of the people on this forum. I’d bet a nickel it’s well below replacement rate.
What ever happened with Covid? How come the hysteria died out?
Turns out… :
1) The lockdowns did nothing to stop the spread, they were simply destroying our economy.
2) The masks were useless and did nothing to prevent transmission of the virus.
3) The IFR of covid was a tiny 0.23%, and that’s not accounting for all the co-morbidity deaths that were falsely labeled as covid deaths.
4) The vaccines did not prevent transmission for millions of people. They did not prevent infection in many cases and numerous vaccinated people have died from the virus. Not only that, but unvaccinated people with natural immunity were better protected than those that took the vaccine and boosters.
5) Studies show that the vaccines cause dangerous side effects at a much greater rate than the CDC admitted.
That every one of these claims is wildly false. Which is what comes of combing your “information” from sources whose agenda has no use for facts. (And I think it also explains the persistent Trump support – most of these people have swallowed lies that stroke their prejudices and have become unreachable).
However, covid concerns have indeed died down. I suspect most of the reason is due to two developments. First, the vaccines have been highly successful, reducing exposure down to “herd immunity” levels. And second, techniques like masks and social distancing are becoming regarded as too inconvenient to bother with when covid cases aren’t seen as much more common than flu cases.
Second of what will be three pieces on Carl Schmitt–including reviews of two fine books, one by David Dyzenhaus, the other by William Rasch.
luckorcunning.blogspot.com
CDC estimates 97 percent of Americans have had covid or the vaccine, or both. The vaccine has not produced anything like herd immunity. What it has done is minimize the risk of death or hospitalization.
Are you from another planet? Covid “vaccines” are no vaccines. My family is living proof and we’re not unique in this respect. They have not been successful and have yet to be investigated for the side effects reported.
There is no correlation between “vaccines” and the sudden drop of concentration camp measures that have failed for three years straight. There’s a correlation with people finally starting to revolt against the tyranny
Moving this here from a different thread where it is off-topic.
keiths, to Erik:
Flint:
Haha. I wondered if you’d be bringing that up again.
I spent over six weeks explaining it, Flint, but you weren’t able to grasp it. I doubt that we’ll have better luck this time around, and I’m not willing to waste much more time trying.
However, it’s been several months since then, and there’s at least a chance that you’ll be able to see it this time. As a courtesy, I’ll make a brief attempt — a very brief attempt — at explaining it again.
The key concept to understand is that two exact numbers can be approximately equal to each other. Consider:
1) π is an exact number with an infinite decimal expansion.
2) 22 is an exact number with an infinite decimal expansion (and all of the digits to the right of the decimal point are zeros).
3) 7 is an exact number with an infinite decimal expansion (and it too has all zeros to the right of the decimal point).
4) The number 22/7 is an exact number with an infinite decimal expansion. No surprise there, since 22 and 7 are also exact numbers.
5) 22/7 is a well-known approximation of π. In other words, the exact number 22/7 is approximately equal to the exact number π.
Do you agree with those five statements? And in general, do you agree that it’s possible for one exact number to be approximately equal to another exact number? If yes, then there may still be some hope. If not, I’ll throw in the towel and accept that you’re probably never going to understand this.
Alan,
In that thread, I explain DNA_Jock’s error in excruciating detail. No way am I going to repeat all of that again.
I have no idea what the issue is here, but all numbers are exact numbers. How could they be anything else? And of course two numbers can be approximately equal to each other, although what “approximately” means varies as to context: 1,000,005 is approximately equal to 1,000, 000 in most contexts, but 5 is not approximately equal to zero.
What is the issue upon which there is disagreement? Can someone explain without digging up long-lost discussions?
aleta:
Exactly (heh). The real numbers are exact by definition, having infinite decimal expansions. They occupy single points on the number line.
Exactitude is a property of a real number on its own. Approximation is not. 22/7 is exact in and of itself, but it is not approximate.
Approximation is relational. 22/7 is approximately equal to the number π, but 22/7 on its own cannot be said to be approximate. It’s exact (and so is π).
The dispute arose in the context of measurement. In the measurement “5.62 inches”, the number 5.62 is a real number and is therefore exact. The measurement is approximate, but the number 5.62 is exact.
Flint and DNA_Jock were unable to grasp that even after more than six weeks of discussion. They believe that since the measurement “5.62 inches” is approximate (or at least inexact, if the measurement is done poorly), the number 5.62 itself must also be approximate or inexact (at least in that context). They even invented an entirely new category of inexact numbers — the “measurement-derived reals” — to be used in expressing measurements. Never mind that these so-called reals aren’t reals at all, and in fact are ranges. Never mind that I provided them with a definition of real numbers that specifies exactitude as a defining property. Apparently mathematicians don’t know what real numbers are, but Flint and Jock do. It’s bizarre.
In reality, the fact that the measurement “5.62 inches” is approximate only means that the exact real number 5.62 is approximately equal to the unknown exact real number specifying the actual length, whatever that happens to be. There is a measurement error, but that error is not part of the number 5.62. Exact real numbers like 5.62 are perfectly fine for expressing measurements. Their exactitude does not imply that the measurements in which they are used are exact. Measurements are approximate, and that is perfectly compatible with the exactitude of the numbers used to express them.
The “measurement-derived reals” aren’t merely misnamed; they aren’t needed at all.
That’s a good explanation, and I agree. A few comments, saying some of this in may own words.
1. Each number is exactly what it is, not another number, with no fuzziness or ambiguity. This is a matter of theoretical mathematics. We commonly write them as decimal numbers that can be expressed as an infinite series, or we think of them as points on the number line to help us describe their unique existence, separate from all other numbers.
2. Measurement brings up a practical, real-world application of numbers. I, and many other high school and college teachers, teach about this explicitly. As you say, “In the measurement “5.62 inches”, the number 5.62 is a real number and is therefore exact. The measurement is approximate, but the number 5.62 is exact.” No measured length is exactly 5.62 inches long; we don’t have the ability to measure infinitely accurately.
Whenever we measure something we explicitly or implicitly assume a range of accuracy. For instance, we might write x = 5.62 ± 0.005 inches to make it clear that we think we are accurate to the nearest 0.005 inches. We might also write 5.615 ≤ x ≤ 5.625 inches. All those numbers are exact numbers that are used to express our best estimate of the length. And in physics class, students are taught to write 5.00 rather than just 5 to make it clear, for instance, that the measurement is 5 to the nearest hundredth.
Making up a new kind of number confuses theoretical and applied math, I think, and is unnecessary. Teaching students about accuracy, the limitations of real-world measurement, and the ways we apply math to those limitations is what is important.
I agree with all of that, and I’m glad you expressed it in your own words. Perhaps two consonant explanations can succeed where a single one failed.
One of the stumbling blocks in the original thread was a failure to distinguish between numbers and their representations. I bring that up because of what you (correctly) say here:
Flint and Jock are confused by the fact that you can use the representation “5.00” to indicate both the value of the measurement and give a hint about its accuracy. They take this to mean that the underlying number differs between the representations “5”, “5.0”, “5.00”, etc. They even go so far as to say that 3 isn’t equal to 3.0, at least not when the latter is a “measurement-derived real”. It’s weird.
In reality, “3”, “3.0”, “3.0000”, “11” (in binary), and “III” (using Roman numerals) all represent the same underlying number and are therefore equal. Additional zeros to the right of the decimal point change the representation, and they can convey additional information in the context of a measurement, but they do not change the underlying number being represented. In terms of their decimal expansions,
3 = 3 x 10^0
and
3.0 = 3 x 10^0 +
0 x 10^-1
and
3.0000 = 3 x 10^0 +
0 x 10^-1 +
0 x 10^-2 +
0 x 10^-3 +
0 x 10^-4
Since adding zero to a number leaves the number unchanged, all of these representations refer to the same number 3 x 10^0, which is exact.
Right. There is an error term associated with both “5.62 inches” and “5.62 ± 0.005 inches”; it’s just that it’s omitted from “5.62 inches” while it’s stated explicitly in “5.62 ± 0.005 inches”. In both cases the “5.62” refers to the same underlying number, which is equal to
5 x 10^0 +
6 x 10^-1 +
2 x 10^-2
In both cases the 5.62 is exact. It’s a real number, after all, and every real number is exact, having one and only one infinite decimal expansion.
Aleta,
I can see where wading through a 28 page thread is unappealing. Although I strongly advise against taking keiths’s precis at face value — his ability to invent a self-serving narrative rivals phoodoo’s.
He ran away, finally.
Here’s a simple question that he resolutely avoided:
It is, I admit, a trap.
I don’t know whether keiths understood the nature of the trap, but he sure squirmed.
Can you spot the problem?
Also fun, we are still waiting for keiths to explain how Karen’s error differs from what he did on that thread with his “0.01194… smoots” claim. It’s been 173 days now.
DNA Jock, I have absolutely no interest in getting involved is some dispute you have with keiths that has a long history.
But you wrote this:
A) 5,93 is an exact number
B) 5,928599201766 is an exact number
C) 5,93 is a reasonable approximation for 5,928599201766 because the percentage difference between them is sufficiently small (it is less than 0.024%)
I assume you are using the British convention of commas for the decimal point. True?
If so, your first two statements are true. And yes, there is about a 0.024% difference between them.
However, whether this is a “reasonable” approximation and the percent difference is “sufficiently” small depends on the applied context. If I’m firing a rocket to the moon, that much error might mean I’d miss the moon, and so 5.93 would not be a reasonable approximation. On the other hand, if I’m calculating the diameter of a tree by wrapping a tape measure around the circumference so that the second number has all those digits of accuracy just because pi was used, then that is false accuracy, and rounding off to the hundredth of a foot might be reasonable. I had to work to make sure students understood this concept.
The “reasonableness” of an approximation is an applied math idea, not a theoretical math idea, and depends on the real-world context.
Jock,
I doubt that people will be motivated to read through that thread, though parts of it were pretty entertaining. However, anyone who does read through it will see that my account is correct.
But back to the topic that Flint has (re)raised. Judging by his comment, he still thinks that it’s problematic to use real numbers (which are exact by definition) to express measurements (which are approximate or inexact by nature). You espoused the same idea in the old thread. Do you still believe that, or do you now accept that it’s perfectly fine and routine to express measurements using exact real numbers, as aleta and I have explained?
aleta, to Jock:
There’s a funny story behind that. Jock calls it “Germanic notation”, and he borrowed it from the Europeans in order to distinguish real numbers from his newly-invented “measurement-derived reals”.
In Jock’s “Germanic notation”, “3,0” refers to the real number that you and I (and the rest of the Anglosphere) would write as “3.0”, while “3.0” is reserved for the corresponding inexact (and completely unnecessary) measurement-derived real. In other words, Jock would record a 3.0-inch measurement as “3.0 inches”, but he would write the abstract number 3.0 as “3,0”.
So Jock not only invented a superfluous category of numbers and misnamed it the “measurement-derived reals” — he also borrowed a European notational convention in order to distinguish his invented numbers from the true real numbers.
Nuggets like these are why I say that parts of the old thread are pretty entertaining. 🙂
On the question of whether two given numbers can be regarded as approximately equal, it’s important to distinguish between the concepts of “approximately equal” and “sufficiently close”.
Here’s how I put it in the old thread:
It’s possible to judge two numbers as being approximately equal without knowing what they represent or what they are being used for. Borrowing Jock’s numbers, imagine we fashion two dowels, one being 5.93 inches long (or as close as we can get to that) and the other being as close as we can get to 5.928599201766 inches long. We show them to a large sample of people, without specifying what we intend to use the dowels for, if anything, and we ask whether they are about the same length. I predict that the vast majority of people will say that yes, the dowels are approximately the same length, despite not knowing their intended use.
We could do the same experiment using lines drawn on paper or plotted on a computer monitor, and I predict that the results would be the same. In other words, people can judge that 5.93 is approximately equal to 5.928599201766, independent of context, just as they can judge that 22/7 is approximately equal to π.
However, whether they are sufficiently close is a separate question that depends on context, as my interferometer example shows. If you ask someone whether 22/7 and π are sufficiently close, the correct response is “sufficiently close for what?”
“Approximately equal” and “sufficiently close” are separate concepts.
May your children live in entertaining times.
If I am going to lose several weeks of my life arguing, I would prefer it be over something important.
Big end vs little end.
Aleta is astute enough to notice that you did not answer the question, keiths.
Still no explanation re Karen’s error either. 😀
DNA Jock, I don’t get it. Let’s leave keiths out of it. Do you agree with my comment that “reasonable” approximation and “sufficiently” close depend on the real-world context, and are not words that apply to pure mathematics?
And other than this distinction, I see no “trap” in what you wrote. What’s the trap? Please explain.
Although, now that it has been explained to me how you use 5,3 and 5.3, I agree that is a useless distinction.
What I find interesting and immensely ironic, considering the stated ethic of this site, is the resolute disrespect for the intentions of those with whom we spar. The complete denial of good will. The complete unwillingness to assume another’s point of view.
We simply must have another nonce rule for commas.
What is a “nonce” rule?
And, without any reference to all these old discussions, I’m curious what you think, petrushka: do you think it would be useful to have a written distinction between numbers in pure mathematics and numbers that are measurements of things in the physical world?
I think it’s quite clear to almost everyone that the conventions for presenting data in scientific publications are just conventions, and not applicable to number theory.
Talking past one another is not discussion.
I see what you meant by “nonce” rule, I think.
I’m not clear about your other sentence. All of the ways that we write about numbers are conventions in that they have been invented and adopted for clarity and consistency. But the issue goes beyond scientific publications. A carpenter, for instance, knows that no measurement is exact but knows very well what level of accuracy is necessary for various jobs (it’s different for sheetrock than it is for window trim).
And I assume by “number theory” you are referring to pure mathematics in general, in which we assume that all numbers are exact.
So I think you are saying, but correct me if I’m wrong, that people understand these distinctions, and that there wouldn’t be any need for a new rule – new conventions – about how we write numbers.
Am I understanding you correctly?
petrushka,
I certainly hope no one lost weeks of their life arguing over this. When you are engaged in a discussion at TSZ, do you treat it as a full-time job? For me, life goes on in parallel. I just drop in periodically to see where the discussion stands and whether someone has posted something I want to respond to.
Is time spent in debate at TSZ worthwhile? I suppose that depends on your reasons for participating. Some people spend hours wandering the landscape, knocking white balls into holes, purely for fun. Others argue on the internet. Is recreation a waste of time?
Also, some of what we discuss here at TSZ actually matters. It matters whether ID is regarded as science and taught to our children in school, and it matters whether we teach them to use a new number system and new notation to express measurements when the current system works just fine. Granted, no one is likely to seriously consider incorporating the “measurement-derived reals” into the curriculum, but it’s still worth stating why Flint and Jock’s proposal is a bad idea.
The topic is also intellectually interesting and pedagogically valuable. Flint and Jock didn’t (and seemingly still don’t) know that all real numbers are exact, and that despite this it is nevertheless perfectly fine to use them to express approximate measurements. That’s a worthwhile lesson.
Finally, there’s the entertainment value of seeing two adults, both technically trained, seriously arguing that we can’t say whether “3.0 = 3.0” is a true statement, and earnestly contesting the idea that the real numbers are single-valued and infinitely precise, despite the consensus of the mathematical community.
Thanks. That is clarifying. I very seldom post here, but I do lurk, and I knew nothing about this past discussion with keiths, jockdna, and others until keiths mentioned something about exact numbers. I’m interested in math, so I responded to that and have had a few things to say.
But I agree with your summary of the situation.
petrushka:
I couldn’t have reached the conclusion that Flint and Jock are wrong about this stuff, nor could I have formulated cogent arguments against their positions, without carefully considering their perspective.
True, but disagreeing over substantive issues is discussion. Whether 3.0 is equal to 3.0 is a substantive disagreement (though a bizarre one). Whether real numbers are exact, and whether they can be used to express measurements, are substantive issues. Beyond those, there are probably a dozen or more substantive disagreements in that thread, including (believe it or not) whether it’s “horrendous” to record a 9-foot measurement as “9 feet”.
We aren’t talking past one another. We’re disagreeing.
Ooops. I see that two posts above I thought I was responding to petrushka but I was really responding to keiths. There are a couple of confusing things about the format of this discussion forum. The author of a comment is in small light print, but then keiths started a quote with petrushka’s name and I thought the comment was by petrushka. And comments aren’t numbered so you can’t refer to them.
So at this point I’m interested in jockdna’s response to my comment at August 19, 2023 at 1:24 pm, if he returns to it.
Ah, the comments are numbered, unfortunately the number is invisible
You can also copy and paste the link (in this case : http://theskepticalzone.com/wp/sandbox-4/comment-page-90/#comment-297446)
into the usual [a href=”link”]link name[/a] changing square brackets to carets.
ETA, the link in the date/time of a comment
Thanks to aleta for demonstrating how to make a point clearly, concisely, and without the aid of a superfluous appendage.
(Oxford commas, should we?)
Question for aleta (just for fun)
Do you think mathematics is real or fictional?
I’m all for Oxford commas, and use them regularly. That’s a subject I’m willing to address.
I tend to take your side on the number argument, but the quantity of verbiage gets tiresome.
When your interlocutor fails to see or accept your point, there is no discussion.
Repeating the argument adds nothing.
There are discussions about factual issues, and disagreement can proceed as if at trial.
There are arguments about morals and values.
But the number argument seems to be about definitions. Tomato tomahto.
Depends on whether numbers are waves or particles.
Yes, I agree with you here. keiths thinks otherwise, writing
nor knowing where they came from, per keiths.
You ask
Certainly: any one who thinks that
is a sound argument is in for a nasty shock. You don’t, so no nasty shock for you, but keiths spent three whole pages arguing this very argument, but he knows there’s a trap, so he won’t answer.
It turned out to be quite helpful when the topic of conversation is whether the infinitely-precise-real 2,7 (of pure mathematics) behaves in the same manner as the measurement-derived-real 2.7 (of applied math). By way of example, 2,7 – 2,7 = 0,0 always, but 2.7 – 2.7 is going to have an error distribution. We could have given them letter suffixes, I guess.
You and I may disagree about the precision of numbers in applied math, but that’s cool.