They Also Mentally Calculated Faster Than a Brain Could Ever Do

The credibility of claims that mathematical calculation comes from brains is inversely proportional to the speed and capacity and reliability at which things can be mentally calculated. There are numerous signal slowing factors in the brain, such as the relatively slow speed of dendrites, and the cumulative effect of synaptic delays in which signals have to travel over relatively slow chemical synapses (by far the most common type of synapse in the brain). As explained in my post here, such physical factors should cause brain signals to move at a typical speed very many times slower than the often cited figure of 100 meters per second: a sluggish "snail's pace" speed of only about a centimeter per second (about half an inch per second).  Ordinary everyday evidence of very fast and accurate math calculation is therefore evidence against claims that unaided human math calculation occurs because of brain activity, particularly because the brain is totally lacking in the things humans add to constructed objects to allow fast recall (things such as sorting and addressing and indexes). Chemical synapses in the brain do not even reliably transmit signals. Scientific papers say that each time a signal is transmitted across a chemical synapse, it is transmitted with a reliability of 50% or less.  (A paper states, "Several recent studies have documented the unreliability of central nervous system synapses: typically, a postsynaptic response is produced less than half of the time when a presynaptic nerve impulse arrives at a synapse." Another scientific paper says, "In the cortex, individual synapses seem to be extremely unreliable: the probability of transmitter release in response to a single action potential can be as low as 0.1 or lower.")  The more evidence we have of very fast and very accurate calculation occurred by humans unaided by any devices,  the stronger is the evidence against the claim that human math calculation occurs from brain activity. 

It is therefore very important to collect and study all cases of exceptional human mathematics performance. The more such cases we find, and the more dramatic such cases are, the stronger is the case against the claim that unaided human math calculation is a neural phenomenon. Or to put it another way, the credibility of claims that math calculation is a brain phenomenon is inversely proportional to the speed and reliability of the best cases of human math  performance.  The more cases that can be found of humans that seem to calculate too quickly and too accurately for a noisy address-free brain to ever do,  the stronger is the case that human thinking is not a neural phenomenon but instead a spiritual or psychic or metaphysical phenomenon.  My previous post "They Mentally Calculated Faster Than a Brain Could Ever Do" described many such cases, as did my post "They Too Mentally Calculated Faster Than a Brain Could Ever Do." Now let us look at some more cases of this type. 

Some cases of exceptional math performance can be found in the book The Great Mental Calculators by Steven B. Smith. Below from page 179 are the results of very hard math calculations by Arthur Griffith (born 1880):

We see above a record of blazing-fast speed in very hard math calculations.  The "extraction of cube root" referred to is solving the problem: what number multiplied by itself three times gives the supplied number?  The "extraction of a square root" referred to is solving the problem: what number multiplied by itself twice times gives the supplied number? 

A long newspaper article on Arthur Griffith can be read here. We read this:

"While engaged in working a series of tests Griffith multiplied 142,857,143 by 465,891,443 and obtained the product 66,555,920,495,127,349, in ten seconds. He multiplied 999,999,999 by 327,841,277, and had completed the writing of the product, 327,841,276,672,188,723, in nine and a half seconds. Other numbers required a longer time, but in no case was the time needed to complete the multiplication more than thirty seconds. Factors of numbers were called out as quickly as the number was submitted. The fifth power of 996, which equals 980,159,361,278,976, was obtained in thirty-seven seconds. Cubes of large numbers were given without hesitation, and in case the number was not a perfect cube the number which is the nearest perfect cube was given at once."

Using the web site here, I verified that the first  multiplication result is correct. The second multiplication result, 327,841,276,672,188,723, is incorrect only in the fifth-to-last digit, all other digits being correct. We can't tell whether it was a calculation error by Griffith, or an error by whoever wrote down his answer or who typeset the newspaper article. 

On page 297 the author says he was asked by Wim Klein to give two five-digit numbers. The author gave 57,825 and 13,489. In 44 seconds Klein multiplied the two numbers together mentally. On the same page we are told Klein extracted the 19th root of a 133-digit number in under two minutes. 

On page 301 we read this about lightning-fast calculations by Maurice Dagbert:

The same page refers to astounding multitasking and number memorization capabilities of Dagbert:

We read on the next page that Dagbert does not write any intermediate results, but simply announces the number calculated. On page 58 of the book Mental Prodigies by Fred Barton, we have the comment below, which may explain some of Dagbert's abilities. It is a description of something like a photographic memory for numbers:

On page 60 of the same book we read about these "instantaneous" mental calculation feats of Dagbert:

On page 63 of the same book we are told that Dagbert would do performances in which he faced away from a blackboard, and audience members would call out 2-digit numbers that were placed in a grid like the one below. Without  ever viewing the blackboard, Dagbert would correctly name all numbers and their positions in the grid, as well as telling the sum of each of the columns. 

On page 306 of The Great Mental Calculators we read of the astonishing calculation ability of Shakuntala Devi:

In the 1952 newspaper story here, we read of rave reviews of Devi's calculation abilities. A reporter attempts to stump her:

"Your reporter, at this point, slyly glanced at a piece of paper he had laboriously prepared, and asked: 'What is the cube root of 3,375 multiplied by the cube root of 117,649 divided by 5?'

'147,' said Shakuntala, stifling a yawn, and adding, almost apologetically: 'I am usually given problems that present difficulties of one sort or another.' ”

 The answer of 147 is correct. You can get the intermediate numbers in this calculation by using the cube root calculator here, but no such tools existed in 1952. 

On page 311 of The Great Mental Calculators, we learn of the astonishing short-term memory of Hans Eberstark, who could memorize 40 digits after hearing them spoken only once:

According to a page on Guinness Book of World Records, "The most decimal places of Pi memorised is 70,000, and was achieved by Rajveer Meena (India) at the VIT University, Vellore, India, on 21 March 2015."

As a young child, Vito Mangiamele (born in 1827)  was asked: what is the cubic root of 3,796,416? In about half a minute, he gave an answer of 156, which is correct. 

Many a human can calculate as fast as he or she can recall. For example, the Guinness world record web site tells us, "Scott Flansburg of Phoenix, Arizona, USA, correctly added a randomly selected two-digit number (38) to itself 36 times in 15 seconds without the use of a calculator on 27 April 2000 on the set of Guinness World Records in Wembley, UK."  Such speed cannot be explained as the activity of a brain in which signals have an average speed that is literally  only about a snail's pace. 

To give another example, In 2004 Alexis Lemaire was able to calculate in his head the 13th root of this number:

85,877,066,894,718,045, 602,549,144,850,158,599,202,771,247,748,960,878,023,151, 390,314,284,284,465,842,798,373,290,242,826,571,823,153, 045,030,300,932,591,615,405,929,429,773,640,895,967,991,430,381,763,526,613,357,308,674,592,650,724,521,841,103,664,923,661,204,223

In only 77 seconds, according to the BBC, Lemaire was able to state that it is the number 2396232838850303 which when multiplied by itself 13 times equals the number above.  Here we have calculation speed far beyond anything that could be possible if calculation is done by a brain in which signals have an average speed that is only about a snail's pace. 

On page 318 of The Great Mental Calculators book, we are given this account of the mental powers of Shyam Marathe: