obsolete knowledge: mental arithmetic

[Sit Heel Speak]

It still just drives me absolutely batty how you morons can think that nuclear power is acceptable, though. Jesus...don't any of you pathetic fools know about the M-shaped curve of fission-product isotope distribution, and what happens to all that krypton and xenon gas that wafts out from the reactor into the surrounding atmosphere???

Off the topic of the thread, but what do you propose be used instead?
______
Dennis

My answer, back in 1978, would have been the same as many celebrities' of the time, e.g. Jacques Cousteau, Jerry Pournelle, Amory Lovins': Surface-based steam and photovoltaic solar, space-based panel-through-microwave solar, wind, OTEC, hydro, microhydro, tide and wave energy, natural gas, and geothermal--in short, "anything and everything else." Whatever is available and appropriate to local conditions. In this vein (no pun intended) I would like to see coal-burning stopped too.

My answer, circa 2005, would have been: Zero-point technologies such as presently applied by Japan Magnetic Fan, Incorporated. These should get a Manhattan Project program of crash development. Let's prove once and for all whether Nikola Tesla really did build a fuel-less Pierce-Arrow car in 1931.

Today, I believe that the U.S. government knows perfectly well the answer to the Tesla question; and, that answer is yes; and so, the world's present-day nuclear, coal, gas, and hydro electricity-generation grid is, like NASA, one vast dog-and-pony show, serving mainly to distract from, thereby conceal, what the real most-advanced technology is. For electric generation, the several known ways operate on the principle of direct (e.g. magnetic perpetual-motion motors) or near-direct (e.g. burnable water and so-called "cold palladium-catalyzed fusion") conversion over, from the ever-present Dirac sea of quantum vacuum flux.

[Pizzasgood]

space-based panel-through-microwave solar

Yes please. The sun is already one giant fusion reactor just chugging along on its own. It's sitting there dumping out absurd amounts of energy every second. Not putting up a bunch of space-based solar collectors is just wasteful.

[Sit Heel Speak]

space-based panel-through-microwave solar

Yes please... The sun is already one giant fusion reactor just chugging along on its own. It's sitting there dumping out absurd amounts of energy every second. Not putting up a bunch of space-based solar collectors is just wasteful.

Heh...and, even though there have been experiments with 10-to-100-megawatt multi-story-tall solar-heated turbine towers, in Australia, California, and France...the backyard-scale Lapeyre turbogenerator, U.S. Patent 4,069,673, from the mid-70's, has been totally neglected --goes undeveloped and uncommercialized to this day.

Taking as the calculation basis a surplus satellite-TV dish given a mirror-coating as the collector, a plated nickel-black spun-aluminum hollow hemisphere as the heat transfer surface at the up-pointing end, plain water/steam as the transmission fluid, and the usual turbine efficiencies relied-on by race car drivers and the U.S. Navy, I get 2 kilowatts at noon on a cloudy Seattle day, 21 kw at noon in Dubai.

If I had $50,000 and a spare year, I'd build a prototype. Probably sell for a couple thousand, when mass-produced.

I'm amazed that China hasn't already stamped-out a billion of these, using the Three Gorges reservoir for nighttime storage, instead of going with coal.

[Aitch]

SHS, you should be in business with that.....


Nice thread, prehistoric!

I'm afraid I nearly threw the towel in, and got very close to a breakdown, when told at 14 that the maths I had been taught was all wrong, and calculus showed infinity to be both plus and minus

AAGGHH WHAT!......They just split my whole world system asunder!

god fell apart! What madness is this education that can do that to a child?

But I WAS in the UPPER maths group, so HAD to study for applied maths early GCE 'O' level, ......until the near end of term, when they announced
The 'O' level has been abolished, but if you stay on for an extra 2 years you can get early credentials for Uni.....

Some part of me seemed to favour switching off

Something seriously wrong with 'clever people' I mused....

and proceeded to go racing go-karts......ho hum, much more fun and dangerous, but self-controlled

On another tack,....

Here's an interesting timeline, as an intro to another post of mine, which it time-crosses at 2055

enjoy

http://www.kurzweilai.net/articles/art0 ... rintable=1

http://www.murga-linux.com/puppy/viewtopic.php?t=52530

Why wait for some millenniums hence?

Aitch

[cb88]

Actually we use the word maths here in the US as well... only for nonstandard maths (alternate vectorspaces and such) though the regular one is just math plain old math LOL

[Sit Heel Speak]

SHS, you should be in business with that.....

Maybe. But it might turn out to be non-competitive. Looks like someone has come up with a 95%+ efficient solar photovoltaic cell, and China is rapidly expanding its ability to manufacture somewhat lower-tech solar cells. See
http://www.eetimes.com/showArticle.jhtm ... =223000119
http://www.eetimes.com/showArticle.jhtm ... =223000139
http://www.eetimes.com/showArticle.jhtm ... =222300098

The problem with solar cells is, it does not appear feasible to manufacture them fast enough to meet rising energy demand. I suspect the Lapeyre turbogenerator could, though.

...I'm afraid I nearly threw the towel in, and got very close to a breakdown, when told at 14 that the maths I had been taught was all wrong...

I was lucky. I grew up in a Seattle suburb where Boeing was manufacturing the 727 about ten blocks from my high school. Everyone bright was expected to grow up able to design airplanes. So, the school board did not tolerate "new math" and suchlike, at least not til long after I had graduated, with integral calculus under my belt.

...Here's an interesting timeline, as an intro to another post of mine, which it time-crosses at 2055

Kurzweil's batting average as of 2009 was only fair. Especially his forecast of economic expansion...

[prehistoric]

I've just flipped through the standard exposition of the Trachtenberg system, translated and adapted by Ann Cutler and Rudolph McShane. I did not find my ideas for multiplying by using squares. I did find a number of tricks like mine concerning squares, but although he uses the same algebraic basis I do, he always seems to go from multiplication to squares, not vice versa. This is consistent with his determination to avoid memorization of tables.

My own application required very rapid answers good to 1%. I was willing to memorize some numbers, though I had plenty of ways to reconstruct tables if I forgot an entry.

While I was looking through the book, I came across a problem which was supposed to illustrate how well that system works on two-digit numbers. Unfortunately, I had such a straight-forward way of dealing with that problem I never got around to his approach. Here is the problem, with my solution:

73*54 = 73*53+73 = (63-10)*(63+10)+73 = 63*63 - 10*10 +73

or,

3969 - 100 + 73 = 3969 - 27 = 3942

If I didn't remember 63*63 = 3969, I could use the method for finding squares near 50, because I certainly remembered the square of 13.

63*63 = (25 + 13)*100 + 13*13 = 3800 + 169 = 3969

Simply making a quick, rough estimate (a "gouge") is enough for the kind of go/no-go decisions I was making. I could call out the first two digits of the answer without making an exact calculation of all digits. Practice had taught me the squares up to 100, so this appeared to be instantaneous.

Another case where my old habits were handy came up recently in a case of a business alleged to have made a 50% increase in assets in two years. What was the yearly equivalent? This is the same as asking for the square root of 1.5. Remembering that 12*12 = 144 gave me a first estimate of 1.2, while noting that 150 = 12*12.5 gave me an upper bound. Newton's method uses the mean of these for the next iteration, which gave me 12.25 as the approximate square root of 150, or 1.225 as the square root of 1.5. This allowed me to say they were getting about 22.5% growth per year.

A calculator gives 1.2247... which rounds to the nearest 0.1% as 22.5%.

[prehistoric]

Well someone had to burst my bubble.

I was in a bookstore, and picked up a book on "Secrets of Mental Math". I recognized Michael Schirmer's name, and the names of Bill Nye and James Randi, who wrote their own forewords, otherwise I would not have touched it.

Once I got it home and started reading, I ran across this problem in the prologue, describing how Arthur Benjamin does his "mathemagic" act. He asks for people with calculators to bring them on stage for a test, then asks the audience to call out a two-digit number, and another. He gets 23 and 57.

Right away, I'm thinking,

23*57 = (40-17)*(40+17)= 40*40 - 17*17 = 1600 - 289 = 1311

I'll bet this guy is using my squaring trick!

Glancing over the headings I also see he is doing left to right addition/subtraction. This shows up in my handling of the above problem, if I write out one step I failed to mention above:

1600 - 289 = 1600 - 300 + 11

One feature of doing things this way is that you get the first two digits very quickly. In many cases, this is enough for a go/no-go decision -- which is handy if your life depends on quick (correct) results, (as mine once did.)

When someone who knew one aspect of my methods tried to feed me a multiplication problem where the numbers can't be factored, because they are prime, and the difference is large enough to require subtracting 4-digit numbers, I turned it into a very simple problem.

13 * 97 = 13 * (100-3) = 1300 - 3*13 = 1300 - 40 + 1

The intermediate step of introducing that subtraction baffled him. What I gain by this is an answer which arrives as a sequence of values: 1300, 1260, 1261. I can stop as soon as the answer is precise enough.

Many problems only require an order of magnitude estimate to decide if they will work. This was a required skill back in the days of slide rules, (when we weren't dodging velociraptors.) Getting the first digit of the answer correct rules out a lot of other errors. By the time you get two digits correct, you really have done a lot to separate fact from fiction. If you need four or five digits to tell if something will work, it is probably a marginal proposition anyway.

(Incidentally, the first estimate for the value of the cosmological constant based on "vacuum energy", which made a brief guest appearance in this thread, was off by 120 orders of magnitude.)

The book was published in 2006, and this is the first I've heard of it. We'll see what else I can learn.

Added: I learned a number of tricks and techniques, and recommend the book. Unfortunately, it is hard to change many years of habits. However, my methods seem to be good enough, when combined with my general slippery style of dodging hard problems.

An example from the book had to do with squaring three-digit numbers. Using his method, Benjamin placed 359*359 last in the section, because it was the hardest problem yet.

This seemed ridiculous to me. Since I know (36*36)*(10*10) = 360*360, and have a simple rule for the difference of consecutive squares. If I don't remember 36*36, I can use the rule for squares near 50. (I certainly remember 14*14, because 14 is about 100 times Sqrt(2).)

36*36 = (25-14)*100+14*14 = 1100+196 = 1296

360*360 = 129600

360*360-359*359 = 360+359

So, 359*359 = 129600 - 360 -359 = 12960 - 400+40 -400+41 =129600-800+81 = 128881

Moral: it is hard to avoid easy special cases.

[KF6SNJ]

When did the slide rule become obsolete? I still have three of them.

[prehistoric]

When did the slide rule become obsolete? I still have three of them.

I even have a special set for designing multi-stage rockets, but that just shows that I am also obsolescent.

As for the current generation, just wait until their batteries fail.