Mathemagician Video

[rprosperi]

Interesting and entertaining video:

https://www.flixxy.com/lightning-calcula...-magic.htm

[Peet]

Which possible (Voyager) RPN calculator has an x-square button ("allow you to do the calculation even faster") on it?

[Don Shepherd]

(07-19-2021 03:27 PM)rprosperi Wrote:  Interesting and entertaining video:

https://www.flixxy.com/lightning-calcula...-magic.htm

That guy is GOOD!!

[C.Ret]

(07-19-2021 03:49 PM)Peet Wrote:  Which possible (Voyager) RPN calculator has an x-square button ("allow you to do the calculation even faster") on it?

Any programmable HP Voyager in USER mode !

But, squaring an entry is fast and simple on any RPN calculator (programmable or not):
just type-in the number, then press ENTER↑ and the multiplication key.

[Valentin Albillo]

(07-19-2021 03:27 PM)rprosperi Wrote:  Interesting and entertaining video:

https://www.flixxy.com/lightning-calcula...-magic.htm

Very good, Bob, kudos !!

I don't usually watch videos recommended by anyone but being you the one recommending it I made an exception and indeed it was worth it, the guy is really amazing and very funny, I loved all the many puns ("recap", Rain-man impression, etc.)

Thanks for bringing it to our attention, much appreciated.

Best regards.
V.

P.S.: For those interested in people with such abilities, have a look at this Wikipedia article: Zacharias Dase

[Peet]

(07-19-2021 05:14 PM)C.Ret Wrote:  But, squaring an entry is fast and simple on any RPN calculator (programmable or not):
just type-in the number, then press ENTER↑ and the multiplication key.

I guess you didn't see the video. That's only the RPN counterpart to *= but he mentions a dedicated key on the RPN calculator.

[Jim Horn]

Very fun video! I noticed that the fifth two digit number he squared was a multiple of 3, so the square was a multiple of 9 as is the square of that. So the sum of the 7 digit number's digits is also a multiple of 9. By adding the other six called out digits, he could determine the 7th one.

Also, the birthday day of the week calculation can be done with John Horton Conway's remarkable "Doomsday" algorithm. I've used it for years. His calling out the dates by year, month and day is exactly the order used in that algorithm so he could be doing the calculation as the above were called out, yielding the immediate result.

Mental arithmetic - it's fun! Bob Pease once wrote about calculating the common log of 2 in his head to a number of digits. Richard Feynman was known for this skill as well. As someone who celebrated his 25000th day last Friday, I admire those with that skill and try to improve my own.

[Didier Lachieze]

(07-19-2021 03:49 PM)Peet Wrote:  Which possible (Voyager) RPN calculator has an x-square button ("allow you to do the calculation even faster") on it?

Ancient RPN calculator with an x-square button: HP-45, more recent one: HP-33s

[Bill (Smithville NJ)]

Bob,

Thanks for posting the link. A lot of fun to watch.

One item caught my attention when he did the 5 digit square at the end. He said he would be using a word phase to help him and did indeed use "cookie fission".

This reminded me of the great book "Moonwalking with Einstein: The Art and Science of Remembering Everything" by Joshua Foer. This book covers many of the ways to memorize items, such as the sequence of random decks of cards, digits of pi, etc. It's a fantastic book and a great read. The author spent a year training for the USA Memory Championship by researching and learning various memory systems.

73
Bill WD9EQD
Smithville, NJ

[Valentin Albillo]

(07-19-2021 08:24 PM)Jim Horn Wrote:  Mental arithmetic - it's fun![...] As someone who celebrated his 25000th day last Friday, I admire those with that skill and try to improve my own.

I've been also very fond of mental math since I was a teen, and with the passing years I learned a number of easy techniques to help performing a lot of reasonably complex calculations in my head, achieving at least slide-rule precision results (3 significant digits). This would include such things as computing 2^100 or factorials of large/non-integer arguments, things like that. I still can do it, of course.

But another quite interesting topic on mental math I've never seen discussed anywhere is the computations you can do while dreaming !

In my experience, I've been able to multiply a 4-digit number by a 3-digit number and achieve the correct result while in a dream, so though in the dream I used paper and pencil, it was obviously done in my sleeping mind. Most interestingly, a few months ago I was able to invert a 3x3 matrix with one-digit integer elements while dreaming, which is my best dreaming-math achievement so far.

In my experience, one difficulty of doing math while dreaming is that numbers and texts tend to change from glance to glance, as do the covers of books, street signs, underground station names (so you usually get lost when trying to go somewhere) and the like, but if you manage to stay focused you'll successfully complete the operation sometimes.

Another difficulty is that though I can do some math while dreaming, it takes a lot of effort and the operation proceeds very slowly. This amazes me in the dream, because I notice the unexpected effort and the slowness and I can't fathom why is that, since I know I can do these operations at much higher speeds with little effort. It would be a telltale that indeed I'm dreaming but usually I don't take the hint !

Perhaps I could use that as my totem (as per Inception): if I try to multiply two 3-digit numbers using pencil and paper and it takes me a lot of effort, then I'm dreaming.

Best regards.
V.

[EdS2]

(07-19-2021 11:24 PM)Valentin Albillo Wrote:  But another quite interesting topic on mental math I've never seen discussed anywhere is the computations you can do while dreaming !
[examples...]

Excellent!

[Maximilian Hohmann]

Hello!

(07-19-2021 11:24 PM)Valentin Albillo Wrote:  But another quite interesting topic on mental math I've never seen discussed anywhere is the computations you can do while dreaming !

Interesting thought. Personally I can't remember ever dreaming of mathematics. Maybe in the night before an exam, but that's too long ago...

But in my experience a dream is not necessarily following a linear timeline. So it is no suprise that you can solve difficult equations because the result may already be known to you before the equation itself. A bit like in a quantum computer :-)

Regards
Max

[EdS2]

(07-19-2021 03:27 PM)rprosperi Wrote:  Interesting and entertaining video...

Thanks Bob - yes it was! How very lucky to have at least one audience member with a 10 digit calculator!

[Harald]

(07-19-2021 11:24 PM)Valentin Albillo Wrote:  But another quite interesting topic on mental math I've never seen discussed anywhere is the computations you can do while dreaming !

In my experience, I've been able to multiply a 4-digit number by a 3-digit number and achieve the correct result while in a dream, so though in the dream I used paper and pencil, it was obviously done in my sleeping mind. Most interestingly, a few months ago I was able to invert a 3x3 matrix with one-digit integer elements while dreaming, which is my best dreaming-math achievement so far.

In my experience, one difficulty of doing math while dreaming is that numbers and texts tend to change from glance to glance, as do the covers of books, street signs, underground station names (so you usually get lost when trying to go somewhere) and the like, but if you manage to stay focused you'll successfully complete the operation sometimes.

Another difficulty is that though I can do some math while dreaming, it takes a lot of effort and the operation proceeds very slowly. This amazes me in the dream, because I notice the unexpected effort and the slowness and I can't fathom why is that, since I know I can do these operations at much higher speeds with little effort. It would be a telltale that indeed I'm dreaming but usually I don't take the hint !

Perhaps I could use that as my totem (as per Inception): if I try to multiply two 3-digit numbers using pencil and paper and it takes me a lot of effort, then I'm dreaming.

Best regards.
V.

How do you know all this? Usually the second I open my eyes, everything I was dreaming disappears.

There is the exception of nightmares that occasionally did wake me up in the middle of the night when I was a child.
And once, I must have been about 10 years old, my dad gave me the task of calculating resistor values for an Ampere meter. The idea was to have a given analogue instrument with know voltage and current and to put in parallel a series of n resistors to get n different measuring ranges by connecting the positive test lead to taps in-between the resistors. (I'll try and draw a schematic if this doesn't become clear from my explanation.) The idea of this being to avoid switches to change the range.
Anyhow, I tried all day and couldn't figure out how to do it. While lying in bed I finally worked it out, and I think it was shortly after I had fallen asleep. It was all very clear to me. When I woke you the next morning all I could remember that I had found the solution, but not what it was.
It took me several days to find it again.

Cheers,
Harald

[Valentin Albillo]

(07-20-2021 07:43 PM)Harald Wrote:  [quote='Valentin Albillo' pid='150281' dateline='1626737074']But another quite interesting topic on mental math I've never seen discussed anywhere is the computations you can do while dreaming !

How do you know all this? Usually the second I open my eyes, everything I was dreaming disappears.

Well, I usually remember most of my dreams upon awakening. Then, if the dream has been particularly interesting, I choose to remember it in detail so that it won't get forgotten, exceptionally I even write it down in full. Else, I simply forget it.

Some of my most memorable dreams include lucid dreams, i.e., I do realize that I'm dreaming but that realization doesn't trigger my instant awakening, I remain in the dream. In such occasions I usually perform a number of tests (while in the dream) which frequently result in my being truly amazed at the complexity of the human mind. One of the most amazing things is that the environment seems absolutely indistinguishable from real-life no matter how close I look at it or experience it.

But that's fully off-topic (sorry, Bob !) so that'll be all.

Regards.
V.

[rprosperi]

No problem here Valentin, the discussion of doing math in dreams is fascinating. My dream experience is much like yours: I wake up daily recalling the core parts of (the end of?) my dream, and I can think hard to recall it (or write it down) but otherwise it fades as the day goes by, probably gone by noon.

While in many dreams, I'm aware that it's a continuation of a prior scenario/story line, but not necessarily that I'm in a dream; it's more like the setting / circumstances are familiar.

I don't recall ever doing math in dreams, but that's not surprising as math really doesn't interest me much, whereas I do recall lots of maps in dreams and maps are of great interest.

[jlw]

One of the three-digit numbers from the audience that he squared, 457, was 205849, but every calculator I try it on gets 208849. Perhaps he has a couple segments burnt out in that digit... A minute later, 722 squared is 513284, whereas I get 521284--more faulty segments? Oddly enough, the volunteers onstage with calculators "confirmed" his results. Peer pressure?

Later, when he squares a five-digit number and shows us the process, it suggests how he could have made the above errors.

Then again, in at least one of my HP calculator manuals, is the story of Truman Henry Safford, a 10-year-old child prodigy asked to square 365,365,365,365,365,365. A parting shot claimed that no calculator ever made, even theirs, could do that.

[Albert Chan]

(07-24-2021 01:29 AM)jlw Wrote:  Oddly enough, the volunteers onstage with calculators "confirmed" his results. Peer pressure?

No. It is magic

[Valentin Albillo]

(07-24-2021 01:29 AM)jlw Wrote:  Then again, in at least one of my HP calculator manuals, is the story of Truman Henry Safford, a 10-year-old child prodigy asked to square 365,365,365,365,365,365. A parting shot claimed that no calculator ever made, even theirs, could do that.

Actually, it's much easier than it seems, I can do it as well. The ease comes from the fact that this is a especial-form number, namely

365 365 365 365 365 365 = 365 x 1 001 001 001 001 001

To square this number you must square both factors and then find their product. The square of the second factor is trivial, namely

1 002 003 004 005 006 005 004 003 002 001

while the square of 365 is also trivial to do mentally as it ends in 5. Namely, its square is

365^2 = [36 x 37][25] = [36^2 + 36][25] = [1296 + 36][25] = [1332][25] = 133 225

which is trivial to compute very quickly assuming you know the squares of integers up to 50 from memory, which all mental calculators do, myself included. Else, computing the square of 2-digit numbers such as 36 is pretty trivial, too: 36^2 = 36 x 6 x 6 = 216 x 6 = 1296

Now, all you need to do is compute 133 225 times 2,3,4,5 and 6, which againt it's very easy to do due to its especial form once more:

133 225 x 2 = 266 450, 133 225 x 3 = 399 675, etc

Now you keep in mind these six six-digit numbers and add them up correctly shifted by 3 positions each time and minding the carries and there you are:

365365365365365365^2 = 133 491 850 208 566 925 016 658 299 941 583 225

V.

[Steve Simpkin]

(07-24-2021 01:29 AM)jlw Wrote:  ...
Then again, in at least one of my HP calculator manuals, is the story of Truman Henry Safford, a 10-year-old child prodigy asked to square 365,365,365,365,365,365. A parting shot claimed that no calculator ever made, even theirs, could do that.

Quotes from the Introduction section in the HP-45 manual.

"Little is understood about the methods used by calculating prodigies to perform their awesome feats. The method used by 10-year-old Truman Henry Safford, in 1846 to calculate 3653653653653653652 (as described by the Rev. H. W. Adams) shows that difficult problems are difficult even for prodigies—"...he flew around the room like a top, pulled his pantaloons over the tops of his boots, bit his hands, rolled his eyes in their sockets, sometimes smiling and talking and then seeming to be in agony, until, in not more than a minute said he, 133,491,850,208,566,925,016,658,299,941,583,225!"

"Although your HP-45 might not be as much fun to watch, it makes calculating faster and less arduous, because the operational stack and the reverse "Polish" notation used by the HP-45 provide the most efficient way known to computer science for evaluating mathematical expressions."

And from a bit later in the introduction:

"Incidentally, no calculator available today (including ours) can handle the problem given to our child prodigy. Isn't it comforting to know that people can still do things machines can't?"

https://www.hpmuseum.org/hp45.htm