and good evening and the when I was
asked to give this talk and I my hobbies
in mathematics and it struck me that
from very early school to where I am now
and I was born in 1950 you do the math
you sell and old a lot has changed and
when I was first at school and the
emphasis was on doing calculation and
what we what the National Curriculum
even now is saying it mentions work
calculate 10 times for key stage
quarter-sawed a key element not a lot of
it can be pretty tedious and dull and
when I first started out we used to do
things with long division possibly is
still taught and it’s one of the
problems that might be said for me to do
with something like this
Gobbo and what I was asked to do and was
to find out its diameter if it was a
sphere so it gets remelt it gets recast
as a sphere what size would it be it
might be that the teacher had an idea
that he would break in and remodeled all
these gold bars and rolled out I don’t
know so what did I need to know well one
of the things I need to know I need to
know what the way to it was so it’s
thought for kilograms and that in itself
I need a bit more information and other
information I need to know is what the
density of gold is well it’s 19.3 grams
per cubic centimeter
now with that information you can
calculate what the volume is the volume
you can calculate what the diameter of
us here would be so how I would start
out let’s just just take working out
what the volume is p.m. we had to do
this calculation
12400 divided by 92.3 now if you are
dead this these sort of things you might
start thinking quick wins one of the
things you could do is there’s a common
factor to other either other than normal
nominal numerator you can get it smaller
fortunately 1 9 3 is prime and so you’re
stuck you’re stuck we’re doing the long
division and so you proceed in this way
you set it up you put on line 3 on there
you divide that into the first number
you get that that six that’s 1,000 one
five eight are you all familiar with
this
not from getting knots and chairs and
and and you and you go on doing this and
it would take you a bit of time but as
you got down to the bottom of it you
would find you’ve got the answer and put
back the decimal point until we know
what an answer six four two point four
eight seven it’s quite hard work being
going that’s a paper but it’s hard work
and the next thing to to come my way and
was this chat and John Napier and in
1614 he published of paper a mecca the
difficut logarithm canis descriptio a
description of the wonderful law of
logarithms and what he wrote about it
was this he said since nothing is more
tedious fellow mathematicians in the
practice of the mathematical arts then
the great delays suffered in a tedium of
lengthy multiplications and divisions
the finding of ratios and in the
extraction of square and cube roots and
in which not only is there the time
delay to be considered but also the
annoyance or the many slippery errors
that can arise I had therefore been
turning over in my mind by what sure an
expeditious art I might be able to
improve upon these said difficulties so
um if you’ve done this at school you’re
be familiar with it and what he did was
give you a quick refresher and 16 by 8
okay nobody answer that is but you can
do this in a for logarithms you can
express 16 as 2 to the power 4 8 is to
the power 3
and if you subtract the indices you take
4 for 3 you get 1 and it’s 2 to the
power of 1 and that of course is 2 so
that’s how logarithms work apply it to
our problem as our problem and we’ve got
we take the log we’re using base ten
that there’s a base 2 and we take the
log and that’s 5.0 9 3 1 9 3 is 2.2
six and here is his clever bit of
thinking it’s now a subtraction so all I
need to do is subtract one from the
other that’s quite easy to do I get to
point 807 and take that back and I get
the answer six four two four nine now
you might say well where do you find out
what the logs are well every schoolchild
of my age had a set of locules like
these if you’re a bit pretentious you
have the Cambridge and lumetri
mathematic tables and if you really were
a geek you had something like this which
is seven figure and log tables and they
are notes up and they’re all for the
numbers you go to the right page you
look up what numbers go across the
tables find what it was you put it in
here you do your additional subtraction
and then you’d find your the antilog of
that and you get your answer and all the
fun but taking a huge amount of time so
after that you get your answer next
thing that came my way was the spiral if
you struggle these days they’re not very
common and I still have a few at home
that I have to say I’ve rarely use them
and only did really was to mechanize the
log tables on the ruler it’s divided
into logarithms and so by either sliding
it along and reading underneath that you
could either add which would be a
multiplication or doing other way taking
lengths apart you’ll be a subtraction
and it’s a hence a division next thing
to come my way was calculator bliss
absolute this all that hard work and
you’re familiar with calculators you’ve
got bound to have one if you’ve got a
phone you’ve done it without breaking
the back you might have more than one
calculator on the phone and here all you
need to do is that you know you keep
your key in the number one to one
thousand two hundred hundred divided hit
19 point three equals bingo there’s the
answer and who would want to go back to
doing the hard way
certainly so that’s the one thing that
happened coming along also over the
horizon was the spreadsheet and here
what you could do is you could put that
number in one cell under spreadsheet the
next number underneath and then in the
box underneath it you simply said divide
box a by books be and you get the answer
and a very very simple thing to do but
then things have moved on since then and
I don’t know if you’ve ever tried this
what if you typed that calculation one
two four zero zero divided by nineteen
point three into Google as a Google
search that sounds up Daffy doesn’t it
then you would try that you have
excellent well you know what happens not
only does Google return the answer but
it also gives you a calculator you could
go on calculating with that number if
you wanted to do so and it is quite
impressive but we can go a bit further
and what we’ve done so far is we just
been looking at the volume we haven’t
actually done the entire problem so
let’s just sort out the rest of the
problem and we know what I want him is
we know this formula this gives us the
formula of the volume of a sphere it’s
the volume 4/3 PI R cubed R is the
radius and if we substitute in our
number and then we do a bit of
rearrangement we get this thing we’ve
got the diameter is equal to two times
the cube root of three times 64 2 PI /
sm body before pi so we now got the
whole thing we reduced to one
calculation so what could we do with
that
well what if we typed it into this
search engine this
is called Wolfram Alpha whatever we said
this diameter of a sphere or 4006 or 2.5
now we haven’t told it about formulas
all we’ve said is diameter of a sphere
or volumes 6 for 2.5 haven’t given it
any other clues what does it do with it
it brings about the answer and you can
see there that it says the result is 10
point 7 so not only has it understood
the text it’s also recognizing we’re
talking about spheres it knows about
spheres and it knows what the
relationship between the radius R sphere
is and it’s done the whole thing for us
can we get any better than that well
what have we type this into autumn Alva
sold 4/3 PI R cubed equals twelve point
five kilograms divided by nineteen point
five grams per cubic centimeter for R
now note here we’ve done something that
you’re bored about multitudes school
we’ve mixed up units we’ve got kilograms
in there how we’ve got grams in there
what’s he going to do with that it is
going to give us the right answer it’s
understood textually what we’re doing
and it’s this time it’s done the
complete calculation now we’ve had to
break it down a bit we had to help it a
bit who had to explain us a bit how to
do it how far are we from doing this
fifty years we have gone from hand
calculation to computer sporter
calculation
computer if a gold bar was recast as
affair what would its diameter be
if you mean a standard gold bar then the
diameter would be ten point seven
centimeters and that’s happened in my
lifetime and that’s where I think we’re
going that you will have resumed the
ability to put this generic type
question to a computer and have the
answer back and hopefully we will then
have yes thank you
[Applause]
asked to give this talk and I my hobbies
in mathematics and it struck me that
from very early school to where I am now
and I was born in 1950 you do the math
you sell and old a lot has changed and
when I was first at school and the
emphasis was on doing calculation and
what we what the National Curriculum
even now is saying it mentions work
calculate 10 times for key stage
quarter-sawed a key element not a lot of
it can be pretty tedious and dull and
when I first started out we used to do
things with long division possibly is
still taught and it’s one of the
problems that might be said for me to do
with something like this
Gobbo and what I was asked to do and was
to find out its diameter if it was a
sphere so it gets remelt it gets recast
as a sphere what size would it be it
might be that the teacher had an idea
that he would break in and remodeled all
these gold bars and rolled out I don’t
know so what did I need to know well one
of the things I need to know I need to
know what the way to it was so it’s
thought for kilograms and that in itself
I need a bit more information and other
information I need to know is what the
density of gold is well it’s 19.3 grams
per cubic centimeter
now with that information you can
calculate what the volume is the volume
you can calculate what the diameter of
us here would be so how I would start
out let’s just just take working out
what the volume is p.m. we had to do
this calculation
12400 divided by 92.3 now if you are
dead this these sort of things you might
start thinking quick wins one of the
things you could do is there’s a common
factor to other either other than normal
nominal numerator you can get it smaller
fortunately 1 9 3 is prime and so you’re
stuck you’re stuck we’re doing the long
division and so you proceed in this way
you set it up you put on line 3 on there
you divide that into the first number
you get that that six that’s 1,000 one
five eight are you all familiar with
this
not from getting knots and chairs and
and and you and you go on doing this and
it would take you a bit of time but as
you got down to the bottom of it you
would find you’ve got the answer and put
back the decimal point until we know
what an answer six four two point four
eight seven it’s quite hard work being
going that’s a paper but it’s hard work
and the next thing to to come my way and
was this chat and John Napier and in
1614 he published of paper a mecca the
difficut logarithm canis descriptio a
description of the wonderful law of
logarithms and what he wrote about it
was this he said since nothing is more
tedious fellow mathematicians in the
practice of the mathematical arts then
the great delays suffered in a tedium of
lengthy multiplications and divisions
the finding of ratios and in the
extraction of square and cube roots and
in which not only is there the time
delay to be considered but also the
annoyance or the many slippery errors
that can arise I had therefore been
turning over in my mind by what sure an
expeditious art I might be able to
improve upon these said difficulties so
um if you’ve done this at school you’re
be familiar with it and what he did was
give you a quick refresher and 16 by 8
okay nobody answer that is but you can
do this in a for logarithms you can
express 16 as 2 to the power 4 8 is to
the power 3
and if you subtract the indices you take
4 for 3 you get 1 and it’s 2 to the
power of 1 and that of course is 2 so
that’s how logarithms work apply it to
our problem as our problem and we’ve got
we take the log we’re using base ten
that there’s a base 2 and we take the
log and that’s 5.0 9 3 1 9 3 is 2.2
six and here is his clever bit of
thinking it’s now a subtraction so all I
need to do is subtract one from the
other that’s quite easy to do I get to
point 807 and take that back and I get
the answer six four two four nine now
you might say well where do you find out
what the logs are well every schoolchild
of my age had a set of locules like
these if you’re a bit pretentious you
have the Cambridge and lumetri
mathematic tables and if you really were
a geek you had something like this which
is seven figure and log tables and they
are notes up and they’re all for the
numbers you go to the right page you
look up what numbers go across the
tables find what it was you put it in
here you do your additional subtraction
and then you’d find your the antilog of
that and you get your answer and all the
fun but taking a huge amount of time so
after that you get your answer next
thing that came my way was the spiral if
you struggle these days they’re not very
common and I still have a few at home
that I have to say I’ve rarely use them
and only did really was to mechanize the
log tables on the ruler it’s divided
into logarithms and so by either sliding
it along and reading underneath that you
could either add which would be a
multiplication or doing other way taking
lengths apart you’ll be a subtraction
and it’s a hence a division next thing
to come my way was calculator bliss
absolute this all that hard work and
you’re familiar with calculators you’ve
got bound to have one if you’ve got a
phone you’ve done it without breaking
the back you might have more than one
calculator on the phone and here all you
need to do is that you know you keep
your key in the number one to one
thousand two hundred hundred divided hit
19 point three equals bingo there’s the
answer and who would want to go back to
doing the hard way
certainly so that’s the one thing that
happened coming along also over the
horizon was the spreadsheet and here
what you could do is you could put that
number in one cell under spreadsheet the
next number underneath and then in the
box underneath it you simply said divide
box a by books be and you get the answer
and a very very simple thing to do but
then things have moved on since then and
I don’t know if you’ve ever tried this
what if you typed that calculation one
two four zero zero divided by nineteen
point three into Google as a Google
search that sounds up Daffy doesn’t it
then you would try that you have
excellent well you know what happens not
only does Google return the answer but
it also gives you a calculator you could
go on calculating with that number if
you wanted to do so and it is quite
impressive but we can go a bit further
and what we’ve done so far is we just
been looking at the volume we haven’t
actually done the entire problem so
let’s just sort out the rest of the
problem and we know what I want him is
we know this formula this gives us the
formula of the volume of a sphere it’s
the volume 4/3 PI R cubed R is the
radius and if we substitute in our
number and then we do a bit of
rearrangement we get this thing we’ve
got the diameter is equal to two times
the cube root of three times 64 2 PI /
sm body before pi so we now got the
whole thing we reduced to one
calculation so what could we do with
that
well what if we typed it into this
search engine this
is called Wolfram Alpha whatever we said
this diameter of a sphere or 4006 or 2.5
now we haven’t told it about formulas
all we’ve said is diameter of a sphere
or volumes 6 for 2.5 haven’t given it
any other clues what does it do with it
it brings about the answer and you can
see there that it says the result is 10
point 7 so not only has it understood
the text it’s also recognizing we’re
talking about spheres it knows about
spheres and it knows what the
relationship between the radius R sphere
is and it’s done the whole thing for us
can we get any better than that well
what have we type this into autumn Alva
sold 4/3 PI R cubed equals twelve point
five kilograms divided by nineteen point
five grams per cubic centimeter for R
now note here we’ve done something that
you’re bored about multitudes school
we’ve mixed up units we’ve got kilograms
in there how we’ve got grams in there
what’s he going to do with that it is
going to give us the right answer it’s
understood textually what we’re doing
and it’s this time it’s done the
complete calculation now we’ve had to
break it down a bit we had to help it a
bit who had to explain us a bit how to
do it how far are we from doing this
fifty years we have gone from hand
calculation to computer sporter
calculation
computer if a gold bar was recast as
affair what would its diameter be
if you mean a standard gold bar then the
diameter would be ten point seven
centimeters and that’s happened in my
lifetime and that’s where I think we’re
going that you will have resumed the
ability to put this generic type
question to a computer and have the
answer back and hopefully we will then
have yes thank you
[Applause]
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