Curious About Numbers And Math

PODCAST 211: CURIOUS ABOUT NUMBERS AND MATH

RELEASE DATE: SUNDAY, OCTOBER 16TH, 2022

D:  HELLO, AND WELCOME BACK TO THE CURIOUS KID PODCAST.  WE RECORDED AN EPISODE A LONG TIME AGO, IN AUGUST OF 2019 TO BE EXACT, AND IT WAS ONE OF MY FAVORITE EPISODES.  IT WAS CALLED CURIOUS ABOUT TIME.  WE LEARNED ALL ABOUT TIME.  FOR EXAMPLE, WE LEARNED WHY THERE ARE 60 SECONDS IN A MINUTE AND 60 MINUTES IN AN HOUR.  WHAT’S SO MAGICAL ABOUT THE NUMBER 60?  IT’S EASY TO TAKE TIME FOR GRANTED, BECAUSE IT IS SUCH A PART OF OUR EVERY DAY LIVES, BUT WE DIDN’T ALWAYS HAVE A CONVENIENT WAY TO MEASURE TIME.  I ENCOURAGE YOU TO CHECK OUT THAT EPISODE, BECAUSE IT’S SUPER INTERESTING.  OVER THREE YEARS LATER, WE’RE GOING TO COVER ANOTHER TOPIC THAT, LIKE TIME, IS JUST SUCH A BIG PART OF OUR LIVES, IT’S HARD TO IMAGINE THAT THERE WAS EVER A TIME WHEN IT DIDN’T EXIST.  

O:  QUINTUPLE-MAILBAG!

D:  QUINTUPLE-MAILBAG!

“DEAR JACOB AND OLIVIA, WE LOVE YOUR PODCAST!  OUR NAMES ARE LIVVY (8 YEARS OLD) AND CHARLOTTE (5 YEARS OLD), AND WE ARE FROM DEDHAM, MASSACHUSETTS.  WE LISTEN TO YOUR PODCAST WHEN WE ARE IN THE CAR AND WE LOVE LEARNING NEW THINGS.  WE HAVE LISTENED TO ALMOST EVERY EPISODE!  THE QUESTION OF THE WEEK IS OUR FAVORITE PART!  WE HAVE THREE QUESTIONS FOR YOU!  

1 - CAN YOU HAVE THE SAME DREAM, OR NIGHTMARE, MORE THAN ONCE? 

2 - WHERE DO NUMBERS COME FROM?

3 - WHERE DO LETTERS COME FROM?

THANK YOU FOR EVERYTHING YOU DO!  WE ARE SO CURIOUS!

FROM LIVVY, CHARLOTTE, AND KATE (THEIR MOM)”

“HI!  I’M OLIVER FROM NORTH BEACH, MARYLAND.  I’M 4 YEARS OLD.  I WANT TO LEARN ABOUT NUMBERS AND WHO INVENTED MATH.  THANKS CURIOUS KID PODCAST!”

“HI CURIOUS KID PODCAST!  MY NAME IS DAWSON AND I AM ALMOST 8 YEARS OLD.  I LISTEN TO THE PODCAST WITH MY MOM AND MY LITTLE SISTER, USUALLY AT BEDTIME.  IT MAKES ME FEEL REALLY HAPPY!  MY FAVORITE EPISODES ARE THE ONES ABOUT GREEK MYTHOLOGY, AND THE ONE ABOUT LANGUAGES.  I’M CURIOUS ABOUT SUMO WRESTLING, NORSE GODS, AND THE HISTORY OF MATH.

THANK YOU, DAWSON FROM SANTA ROSA, CALIFORNIA”

“HI, I’M ELENA, I’M FIVE YEARS OLD, I LIVE IN FLORIDA, AND I LOVE YOUR PODCAST.  I LOVED THE EPISODE ON HURRICANES, BUT AM CURIOUS ABOUT WHERE NUMBERS CAME FROM.  I’M ALSO CURIOUS ABOUT HOW DO SHRINKY DINKS WORK.  THANKS FOR READING MY E-MAIL!  HAVE A GOOD DAY.  I CAN’T WAIT TO LISTEN TO YOUR NEXT EPISODE!”

“HI.  I AM AVERIE AND I AM 10.  ME AND MY SISTER LOVE LISTENING TO YOUR PODCAST.  I AM REALLY CURIOUS ABOUT MATH.  WHO CREATED IT AND WHY?  

THANKS, FROM AVERIE OF PROVO, UTAH”

O:  HOLY SMOKES.  NOT ONE EMAIL, NOT TWO, NOT EVEN THREE, ALSO NOT FOUR, BUT FIVE FABULOUS EMAILS… HA HA HA.  WE ARE GETTING CURIOUS ABOUT MATH TODAY FOR LIVVY, CHARLOTTE, OLIVER, DAWSON, ELENA, AND AVERIE.  I CAN’T WAIT TO LEARN MORE BECAUSE I LOVE MATH, JUST LIKE MY DADDY.

D:  THAT’S TRUE.  IT’S NOT UNUSUAL FOR YOU TO ASK ME, OUT OF THE BLUE, TO ASK YOU A BUNCH OF MATH QUESTIONS.  SPEAKING OF QUESTIONS, AND MATH, WHAT’S THE QUESTION OF THE WEEK?

O:  DADDY, WHEN YOU WERE FIVE YEARS OLD, YOUR BROTHER BRIAN WAS TWICE YOUR AGE.  TODAY, YOU ARE 41 YEARS OLD.  HOW OLD IS YOUR BROTHER, BRIAN?

D:  VERY INTERESTING QUESTION.  WHILE YOU’RE THINKING OF THE ANSWER, LET’S LEARN ABOUT THE HISTORY OF NUMBERS.  

O:  IT’S HARD TO KNOW EXACTLY HOW LONG NUMBERS HAVE BEEN AROUND, BECAUSE NUMBERS BEGAN BEFORE RECORDED HISTORY, SO THEY’VE BEEN AROUND FOR A VERY LONG TIME, PERHAPS AS LONG AS 50,000 YEARS.    

D:  WHOEVER FIRST CREATED NUMBERS DIDN’T LEAVE ANY RECORDS BEHIND TO EXPLAIN HOW THEY DID IT.  BACK THEN, HUMANS PROBABLY ONLY TRIED TO DISTINGUISH BETWEEN ONE, A FEW, AND MANY.  IT WASN’T NECESSARILY IMPORTANT TO KNOW WHETHER THERE WERE 7 OR 8 OF SOMETHING, BUT IT SURE WAS IMPORTANT TO FIGURE OUT THE DIFFERENCE BETWEEN MORE AND LESS, LIKE WHETHER THERE WERE MORE PEOPLE IN YOUR TRIBE OR THE OTHER TRIBE.  

O:  IN THE 1930’S, AN ARCHEOLOGIST DISCOVERED A WOLF BONE IN CZECHOSLOVAKIA.  THE BONE WAS ESTIMATED TO BE ABOUT 30,000 YEARS OLD.  IT HAD 55 NOTCHES CARVED INTO IT.

D:  THE NOTCHES WERE SIMILAR TO TALLY MARKS YOU WOULD SEE TODAY, BECAUSE THEY WERE ARRANGED IN GROUPS OF FIVE.  

O:  EARLY HUMANS WOULD CARVE TALLY MARKS INTO BONES, WOOD, STONE, AND CAVE WALLS.  

D:  THEY WOULD MAKE A TALLY MARK FOR EACH ITEM THEY WERE COUNTING, AND EACH FIFTH MARK WOULD BE A DIAGONAL LINE GOING THROUGH THE PREVIOUS FOUR LINES TO MAKE A GROUP OF FIVE.  

O:  PREHISTORIC HUMANS COUNTED THINGS ON THEIR FINGERS AND TOES.  THAT’S WHY THINGS ARE USUALLY GROUPED IN FIVES OR TENS.  IT WAS CONVENIENT TO COUNT THINGS BY FIVES AND TENS USING THE FINGERS AND TOES.

D:  BUT HERE’S THE PROBLEM.  COUNTING THINGS ON FINGERS AND TOES IS ONLY GOOD FOR COUNTING UP TO 20.

O:  AND USING TALLY MARKS TO COUNT THINGS WORKS FOR SMALL NUMBERS, BUT IT IS SO MUCH EASIER TO WRITE OUT THE NUMBER ONE MILLION USING THE NUMBER ONE FOLLOWED BY SIX ZEROES, RATHER THAN MAKING ONE MILLION TALLY MARKS.  FOR THAT REASON, TALLY MARKS WEREN’T VERY USEFUL.

D:  ABOUT 5,000 YEARS AGO, THE BABYLONIAN NUMBER SYSTEM WAS CREATED.  IT WAS THE FIRST TIME THAT A POSITIONAL SYSTEM WAS USED TO DESCRIBE NUMBERS.  THAT JUST MEANS THAT YOU CAN MAKE LARGER NUMBERS USING THE SAME FEW SYMBOLS.  

O:  FOR EXAMPLE, THE NUMBER 3 IS A SMALL NUMBER, BUT IF YOU PUT IT IN FRONT OF THE NUMBER 4 AND THEN THE NUMBER 5, THAT 3 HAS A BIG IMPACT.  ALL OF A SUDDEN, THE NUMBER BECOMES 345.  THE POSITION OF EACH DIGIT IN A LARGER NUMBER IS VERY IMPORTANT.  THAT’S HOW A POSITIONAL NUMBER SYSTEM WORKS.

D:  IT WASN’T UNTIL THE 7TH CENTURY THAT INDIAN MATHEMATICIANS CREATED A BASE TEN POSITIONAL SYSTEM.  THAT JUST MEANS THAT THEY HAD 10 SYMBOLS, SIMILAR TO THE NUMBERS ZERO THROUGH NINE THAT WE HAVE TODAY, AND THEY WERE ABLE TO CREATE ANY NUMBER USING THOSE 10 SYMBOLS.  

O:  A KEY FEATURE OF THE NEW SYSTEM WAS THE ADDITION OF THE NUMBER ZERO.  BEFORE THE SYSTEM WAS CREATED, A SPACE WAS USED TO REPRESENT THE NUMBER ZERO.

D:  THINK ABOUT HOW CONFUSING THAT WOULD BE.  LET’S SAY YOU WANTED TO WRITE THE NUMBER 202.  YOU WOULD WRITE A TWO, LEAVE A SPACE, AND THEN WRITE ANOTHER TWO.

O:  IF THE SPACE WASN’T BIG ENOUGH, IT WOULD JUST END UP LOOKING LIKE THE NUMBER 22.

D:  THAT’S RIGHT.  BUT, YOU KNOW WHAT MIGHT BE WORSE?  THE NUMBER ZERO AT THE END OF A LARGER NUMBER.  THE DIFFERENCE BETWEEN 9 AND 90 IS VERY BIG, BUT IF YOU USE A SPACE TO MEAN ZERO, HOW DO YOU MAKE THAT CLEAR, ESPECIALLY WHEN YOU HAVE A NUMBER THAT ENDS IN ZERO?

O:  THANKS TO CONTRIBUTIONS FROM THE INDIANS, ARABS, MAYANS, AND MORE, WE ENDED UP WITH THE 10 NUMBER SYMBOLS WE RECOGNIZE TODAY, FROM 0 TO 9.  

D:  THE NUMBERS WE USE TODAY ARE CALLED HINDU-ARABIC NUMERALS.  THERE ARE OTHER NUMBERING SYSTEMS OUT THERE, LIKE ROMAN NUMERALS AND EGYPTIAN NUMERALS.  UNLIKE THE NUMBERS WE USE, THE ROMAN AND EGYPTIAN NUMERALS ARE NON-POSITIONAL.  

O:  JUST LIKE NUMBERS EVOLVED SLOWLY OVER TIME, MATH WAS THE SAME WAY.

D:  IT MAY HAVE STARTED WITH PREHISTORIC HUMANS GATHERING FOOD FOR THEIR FAMILIES AND TRYING TO FIGURE OUT HOW TO SPLIT THE FOOD FOR EVERYONE IN THE FAMILY, OR MAYBE EVEN EVERYONE IN THE VILLAGE.  

O:  THAT WOULD REQUIRE SIMPLE MATH SKILLS LIKE COUNTING AND DIVISION.  

D:  EVIDENCE OF MATH BEING USED DATES BACK THOUSANDS OF YEARS.  THERE HAVE BEEN CLAY TABLETS DISCOVERED THAT WERE USED OVER 4,000 YEARS AGO TO DO MATH IN MESOPOTAMIA.  THERE IS ALSO EVIDENCE OF MATH ON EGYPTIAN PAPYRUSES.

O:  THAT SOUNDS LIKE A FUNNY WORD, BUT WE LOOKED IT UP.  THE PLURAL FOR PAPYRUS IS PAPYRUSES.

D:  MORE COMPLICATED MATH, LIKE GEOMETRY, ALGEBRA, CALCULUS, AND TRIGONOMETRY DEVELOPED LATER.  MATHEMATICIAN PYTHAGORAS, FOR EXAMPLE, STUDIED TRIANGLES.  HIS RESEARCH LED TO A BETTER UNDERSTANDING OF HOW TRIANGLES WORK, WHICH IS NOW REFERRED TO AS THE PYTHAGOREAN THEOREM.  

O:  ARITHMETIC IS THE OLDEST FORM OF MATH.  IT INCLUDES ADDITION, SUBTRACTION, MULTIPLICATION, AND DIVISION.  

D:  ALGEBRA IS SIMILAR TO ARITHMETIC, BUT IT’S A BIT MORE COMPLICATED.  ALL OF A SUDDEN, UNKNOWNS ARE USED TO REPRESENT NUMBERS, AND THEY ARE IDENTIFIED WITH SYMBOLS, LIKE X AND Y.

O:  THERE IS ALSO GEOMETRY, WHICH INVOLVES MEASURING ANGLES, LINES, POINTS, SIZES, SHAPES, AND MORE.  TETRIS IS A REALLY FUN GAME THAT HELPS BUILD YOUR KNOWLEDGE OF GEOMETRIC SHAPES.

D:  I LOOOOOVE TETRIS.  THERE IS TRIGONOMETRY, WHICH FOCUSES ON THE MEASUREMENTS OF TRIANGLES IN PARTICULAR.

O:  THEN THERE IS CALCULUS, WHICH WASN’T CREATED UNTIL THE 17TH CENTURY.  

D:  CALCULUS IS PRETTY COMPLEX MATH.  TO PUT IT SIMPLY, CALCULUS IS A TYPE OF MATH DEALING WITH HOW THINGS CHANGE.

O:  I LOVE MATH.  IT’S ONE OF MY FAVORITE SCHOOL SUBJECTS.

D:  I LOVE MATH TOO.  I USE IT ALL THE TIME WHEN I DO MY JOB AS A PHARMACIST.  IT WAS SO MUCH FUN LEARNING MORE ABOUT THE HISTORY OF NUMBERS AND MATH TODAY.  LET’S GET TO THE QUESTION OF THE WEEK.  I HAVE A BROTHER BRIAN… TRUE STORY.  MY KIDS CALL HIM TACO BURRITO… THAT’S ALSO A TRUE STORY.  OLIVIA WAS ACTUALLY THE ONE WHO GAVE HIM THAT NICKNAME YEARS AGO.  ANYWAY, WHEN I WAS 5 YEARS OLD, BRIAN WAS TWICE MY AGE.  NOW I AM 41 YEARS OLD.  HOW OLD IS MY BROTHER BRIAN?

O:  HE WOULD BE 46 YEARS OLD TODAY.  IF HE WAS TWICE YOUR AGE WHEN YOU WERE 5, THAT WOULD HAVE MADE HIM 10.  IF HE WAS 10 AND YOU WERE 5, THAT MEANS HE’S 5 YEARS OLDER THAN YOU.  SO, IF YOU’RE 41 YEARS OLD TODAY, THAT MAKES BRIAN 46 YEARS OLD.  

D:  NICE JOB WITH THAT MATH.  WELL, THAT’S A WRAP FOR THIS WEEK’S EPISODE.

O:  211 - NUMBERS AND MATH.

D:  GREAT JOB OLIVIA, AND GREAT JOB LIVVY, CHARLOTTE, OLIVER, DAWSON, ELENA, AND AVERIE FOR GIVING US A GREAT TOPIC SUGGESTION THAT WE COULD COUNT ON FOR LOTS AND LOTS OF LEARNING.  BEFORE WE SAY GOODBYE, WE HAVE A COUPLE OF SUPER DUPER PEOPLE TO THANK.

O:  WE WANT TO THANK OUR NEWEST PATREON SUPPORTERS, KHLOE AND DECLAN C. AND BRYSON AND QUIN.  

D:  A BIG THANKS TO KHLOE, DECLAN, BRYSON, AND QUIN FOR THE SUPPORT.  WE HAVE THE BEST LISTENERS IN THE WORLD, AND IT’S THE SUPPORT WE GET FROM ALL OF YOU THAT KEEPS THIS PODCAST ROLLING RIGHT ALONG.  JOIN US NEXT WEEK WHEN WE WILL GET CURIOUS ABOUT ALLIGATORS AND CROCODILES FOR LISTENERS IN THE PACIFIC NORTHWEST, QUEBEC, ONTARIO, INDIA, AND AUSTRALIA.  AS ALWAYS, THANK YOU SO MUCH FOR LISTENING AND GETTING CURIOUS WITH US.