scientists as superstars

Those are both rather at odds with reality. Firstly, 'divide by zero' is a canard. Never happened, never going to happen; that's a precise description one will never see, and not a usable reference AT ALL. And, math is NOT just neurons; lots of critters have neurons, only humans seem to have formal math.

Mathematics does have formal principles, but 'a precise way of expressing' has completely eluded the workers in that field. There's useful mathematics from sources that span millennia and continents, in languages which live, struggle, or have died or trasformed. Mathematical typesetting requires multiple alphabets. And lots of pictures/glyphs. The Babylonian-era cuneiform geometry texts in the British Museum are... comprehensible. Color would help, though.

And the NAMES are a mess. I tried to look up a useful property in complex analysis, that generalizes functions of real numbers into the complex domain. That property is called 'analytic', or 'entire', or 'integral', and a few other things. Another property we're all familiar with, is 'uncorrelated' or 'orthogonal', or 'perpendicular', depending on context.

That's why the OEIS Online Encyclopedia of Integer Sequences) has been such a smashing mathematical success: there's multi-language agreement on using Arabic numerals, so (at least for integer sequences) one can RECOGNIZE THE WORK that is published on the topic at hand. And, you can do an online search for an integer sequence, though the language descriptions of other mathematics are still remarkably... disparate.

On a sunny day (Sun, 28 Jun 2020 10:30:56 -0700 (PDT)) it happened whit3rd wrote in :

Yes, you describe a well known problem. I come across it sometimes when writing code, 'translation' of mathematical scribblings to code. Still it (math) is nothing 'real', it is just an isolated reality. Always an approximation of reality and so always incomplete. Just a sub-circuit in the neural net (yet an other one). It is elevated by some of its devotees to divinity, but is just a trained game. As to math, it is universal; crows for example (bird brains if you will ;-) ) also do math:

those birds do not scribble things down so much though. Without direct feedback from reality it becomes a dream, trap..

Contour integration comes pretty close to a controlled form of dividing by zero - epsilon close to it in fact in the limit as eps -> 0.

Even has real applications to filters and feedback loop stability.

There are a few other species around with the concept of number. But AFAIK none have developed any form of written language or notation.

ISTR they have proved to their present satisfaction that any complete description of all of mathematics must necessarily be incomplete.

That is the problem with natural language too many ways of saying almost the same thing but with potential nuances and ambiguities lurking in every corner. It makes specifications for computer programs very tricky.

Theoretical physicists tend to be more interested in does it get the right answer than "can we prove it from first principles". My friends doing mathematics spent most of their first term proving that 0 != 1

There are only really two competing notations for calculus and we should all give thanks that Liebnitz's differentials won. A few places today still use Newton's f, f' anf f" etc to indicate derivatives though.

--
Regards, 
Martin Brown

On a sunny day (Mon, 29 Jun 2020 22:18:39 -0700 (PDT)) it happened snipped-for-privacy@yahoo.com wrote in :

Could not read that link all to the end, what a leader :-( of a poor country held hostage by a group claiming racism to get their ways. I made this joke or is it observation? prediction? in an email to someone here last week, freely translated: 'The reason the US does not have a large military parade like Russia's 75 year victory parade is that half of the troops would kneel'.

The empire is no more, as all empires before it it succumbs under its own weight and what's the word 'degeneration'?

A clown leading, the blind leading the blind, imagine a clueless clown leading research into electronics.

And then complain when China makes better products, and lockup the family of the Huawei founder, bully other countries into not using those better (than US makes) products giving you an inferior commie-nuke-ation system and so you be obliviated.

Maybe you have never been to what you call 'the rest of the world'? I have and US did not score very high. Some of it is in my view, a joke, like donald (not the duck, that was at least fun to read some of the time).

But the system freezes accumulated knowledge (or more often, accumulated mistakes) and punishes dissent. Big new ideas come from hereics. I was just reading about how a kid used daddy's money to invent the Hexfet; that's in the AoE Xfiles book. He's why we have

2N7002s.

This is a good book, but I don't understand what it's about.

What it says to me is that caveman, and social structures since, fight to defend themselves from ideas. Our progress has consequently been slow and incremental, thousands of years behind what was possible.

There is a very real Deep State that supresses freedom, and it's a lot bigger than is was in 1789.

--

John Larkin         Highland Technology, Inc 

Science teaches us to doubt. 

  Claude Bernard

Not necessarily /state/. Entrenched interests/wealth/power usually does do that.

Some states/governments are progressive and enhance and widen opportunities.

To me, the Deep State is not some mystical evil society. It is the large, loosely allied, and increasing fraction of society that derives its income and power through the application of law, and who pay for the politicians who write the laws.

So far, technology has increased the productivity of us, the dairy-cow part of society, enough to keep up with the Deep State. But that may not continue indefinitely.

--

John Larkin         Highland Technology, Inc 

Science teaches us to doubt. 

  Claude Bernard

It isn't a mystical evil society to me either.

I suspect there are as many "definitions" of "deep state" as there are people writing about it.

That kind of fuzziness is really useful to those trying to turn vague feelings of discontent about life into raw anger/fear/etc.

Really? Examples, please.

Sometimes. Einstein had a few, but he wasn't a heretic.

Hexfets are International rectifier parts. It's one of their trademarks.

The 2N7002 is described as Trench FET and is supplied by NXP and ON-Semicon ductor (which used to be Philips Semiconductor and Motorola).

n_title?ie=UTF8&psc=1

Probably because lots of new ideas are bad ideas.

What might have been possible if people only had good ideas?

The obvious example is the one paid for by the Koch brothers, that astro-tu rfed the Republican Party into the Tea Part Faction, who couldn't find a pr esidential candidate more attractive than Donald Trump in 2016.

It's too ineffective to suppress freedom directly, but it has made a nasty mess of the USA, which was never all that democratic or free (unless you ha d a great deal of money) and now seems to be working hard on becoming a fai led state.

The US response to the Covid-19 epidemic is remarkably inept - 44,734 new c ases today. The death rate hasn't started climbing yet, but that's probably only a matter of time.

The US population is eventually going to work out that a more competent gov ernment could have prevented most of the Covid-19 deaths, and they may star t looking for a way of getting one. You go overseas to get stuff built - ma ybe you'll start subcontracting your administration too. Trump's already do ing what Putin thinks best, and it wouldn't be difficult to find somebody m ore competent than Putin.

--
Bill Sloman, Sydney

Oh that's just CNN. They're a deranged hate-site.

President The Donald has been excellent--lots of jobs, employment for the downtrodden--it's just that lefties hate that.

Obama planted much of this before he left.

I've been around the world and lived overseas.

It has been my experience that the s-hole countries around the world all had one thing in common: they steal from one another. Either with the club, or possibly worse, with the ballot.

Polities who believe their government's fundamental purpose is taking and giving, fare poorly in some (dis)proportion to the taking and giving.

Cheers, James Arthur

Have you thought that through?

How are these governments enhancing and widening opportunities?

Cheers, James Arthur

I've not only thought it through, I've witnessed it.

I refer you to Germany, the UK, and similar from the 60s onwards.

But you didn't answer my question, you've merely made a vague statement of 'goodness' and posited a vague causation, to unidentified policies.

What did they do that enhanced and widened opportunities?

Cheers, James Arthur

Many things. I'll mention two related to education. The Open University (think MOOC half a century ago). Ensuring underprivileged kids got the best education based on their abilities, not their parents' class[1].

But you won't believe anything that doesn't fit into your weltanschauung, so there isn't much point in my spending my time trying to open your eyes.

[1] realise that class in the UK is similar to race in the USA

That's constructive--class-based discrimination is wrong.

In America, national teachers' unions are devoted to ensuring that poor children be compelled to attend their schools, no matter how awful the school.

I'm very persuadable, but it has to make sense.

If you try and tell me handing out money fixes poverty, you're going to have a tough time explaining how, and rationalizing why sixty years of that has only made things worse in the US.

We discriminated heavily, years ago, and we ended that, generations ago. Anyone who wants to can get a job now. And getting a job is virtually all one needs not to be poor.

Cheers, James Arthur

Eliminating (or greatly reducing) poverty is no easy matter. You are right that education plays a key part.

USA has a particular challenge in that it has such a money-dominated culture. Tom is wrong to say that race is the American equivalent of British "class" - while race has a solid part to play, it is /money/ that makes class in the USA. People associate very little with others outside their monetary class, and the possibilities for moving upwards in monetary class are very small. (Not non-existent, of course, but small - and smaller than they used to be.)

Poverty is not about not having money in absolute terms - it's about having less than others, and less than you need for your basic needs. There are plenty of Americans who have two jobs but get their food from food banks. There are plenty of families with two working adults that can't afford to pay their rent. A job is /not/ enough to avoid poverty. The cost of living, the cost of a place to stay, is critical. Having enough time left over besides work to look after your family, keep yourself healthy, have a life - that is all important.

As poverty is primarily a relative term, the key to dealing with it is improving equality. If an aspect of life can be disassociated from money, poverty is reduced. The biggest one here is health care - universal free health care is an absolute requirement because it stops (or at least reduces) the cycle of poverty leading to poor health leading to more poverty. This is followed by education, with a similar cycle but over a longer period (generations rather than years). Then comes housing. Council housing schemes don't give you the nicest place to live, but they give you something you can afford and you are not forever in fear of the landlord.

And /equality/ is vital to this. In the USA, you are very keen on means-testing - people can get support for health or other things if they can prove that they can't afford to buy it themselves. In countries that try to get a more equal society, it is the same for /everyone/. It doesn't matter if you own a huge company or you've never been able to hold down a job - you have the same right to health care in the same hospital, your kids go to the same school and you get the same child benefits for them. Everyone feels society is supporting them, while you contribute according to your income. If you don't have this levelness and equality, you have a system where the rich are forced to give charity to the poor, which is resented by everyone.

That is true /as well/.

The snobbishness/fear that the higher orders have of the lower orders is - to a useful /approximation/ - based on class in the UK and race in the USA.

Apart from that, we agree.

I doubt that dagmargoodboat will be persuaded by any words, though. Hence my decision not to bother trying to enlighten him.

You missed out Japan. Anywhere in fact that tries hard to educate all of its population to their full potential irrespective of race or class.

Ensuring that a good quality education is available to *everyone* and not just to those who are rich enough to pay for it. Admittedly in the UK there is an even better education available to the very richest who typically go on to be hellraisers at university and then politicians.

--
Regards, 
Martin Brown

I've no experience of Japan, but it seems reasonable to include it in my "and similar".

Well, I was offered a scholarship at a local public (i.e. fee paying for furriners here :) ), but chose to go to the local state grammar school. Never had any cause to regret that! Of course my parents had chosen where to live based on having a local decent school.

As it was memorably put...

?We class schools, you see, into four grades: Leading School, First-rate School, Good School, and School. Frankly," said Mr Levy, "School is pretty bad...? ? Evelyn Waugh, Decline and Fall