Posted on 10/22/2019 2:00:33 AM PDT by LibWhacker
I assume this means that computer algorithms will compute faster, meaning software can be written that is faster and more efficient, speeding computers up without boosting IP the hardware.
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I’m not sure. Don’t computers do something like bit shifting for multiplication? Too bad the article didn’t make it clear.
Think what the calculus has done for us. It took well over a thousand years to come up with it.
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The bits and pieces of calculus were known during that time, such as the method of exhaustion.
Would Newton and Leibniz have developed calculus if there weren’t physics problems they wanted to solve?
Math languished for centuries until Christian Western civilization found a need to develop it more.
Applications of the Schönhage–Strassen algorithm include mathematical empiricism, such as the Great Internet Mersenne Prime Search and computing approximations of π, as well as practical applications such as Kronecker substitution, in which multiplication of polynomials with integer coefficients can be efficiently reduced to large integer multiplication; this is used in practice by GMP-ECM for Lenstra elliptic curve factorization
I doubt it will have any practical effect on routine calculations. Computers use hardware multipliers that are effectively just like the multiplication tables you learned in school, just with bigger tables. The resolution of most practical calculations is far less than few score decades. For instance expressing the national debt to the nearest penny only requires sixteen digits, currently about $22,920,314,419,523.31. The total number of seconds since the birth of Christ can be express with 11 decimal places, currently 63,739,036,477.
The expense of applying “faster” algorithms probably will never be cost effect on these scales. This kind of math is only useful for things like number theory and its cousin cryptology.
btt
Actually, there are an infinite number smaller as well.
“For most of us, the way we multiply relatively small numbers is by remembering our times tables – an incredibly handy aid first pioneered by the Babylonians some 4,000 years ago.”
Let me update the above:
“For most of us, the way we multiply relatively small numbers is by remembering our times tables – an incredibly handy aid first pioneered by the Babylonians some 4,000 years ago, but NO LONGER considered necessary by today’s ‘enlightened’ public schools (the same schools that most conservatives send their kids to) in the United States which instead rely on ‘technology’ to do the calculations.”
re: “Think what the calculus has done for us. It took well over a thousand years to come up with it.”
LOST in time: The Antikythera Mechanism.
re: “Mathematicians Have Discovered an Entirely New Way to Multiply Large Numbers”
Adding. Logarithms. ?
Another game in search of grant $$$$$$.
Mathematicians Have Discovered an Entirely New Way to Multiply Large Numbers
It is called Common Core.
Any answer is correct..... : )
Infinity plus one! Ha!
“How will they know it’s correct?”
Like many of us who took high school math, we had to show our proof, unlike me who usually answered choice C and had a 25% chance the answer was correct.
Computers will just continue using the shift and add method required of binary numbers. It takes a maximum number of operations as there are bits in the number.
No, I need more than three significant digits.
Well duh...
Some hardware uses more exotic logic where multiplication is done using the same technique, but no clocking is needed. For that hardware the time is known as propagation delay.
I was a little too glib. I confined myself to positive integers. There are no general algorithms that allow one to multiply irrational numbers*. There is no way to multiply pi by two because there is no exact way to express pi in a finite number of digits. In computers irrational numbers are always approximated by some binary fractional expression.
*Infinite repeating fractions can be expressed as rational numbers, of course, and algebraic numbers (like phi, for instance) can be expressed as other algebraic numbers.
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