TOK Essay:
I agree to a certain extent with the claim: “all models are wrong, but someare
useful” as this can be seen through the Areas Of Knowledge of Mathematics and
Natural Sciences. Itisessentialtounderstandwhatamodelisasitwillhelpguidethe
discussiononwhetherallmodelsareconsideredwrong.Amodelisgenerallyknownas
a visual representation of a proposed structure to help predict a trend
(Merriam-webster). However models may appear as wrong as they are merely
“approximationsofreality”whichcanlimittheirusage(“AllModelsAreWrong”).Itisalso
importanttoacknowledgethatthisclaimstatesthatallmodelsarewrong,whichmeans
that the whole quantity of models that exist and will further exist in the future are all
incorrect. Fundamentally, it is important to understand how wrong the modelshaveto
be in order to be considered ‘not useful’ (“AllModelsAreWrong”).Tofurtherdiveinto
this question, I will be exploring this through the usage of mathematical models and
biological models.
Mathematics is a great example to demonstrate how models canbewrongbut
useful simultaneously. For example we can analyze the usage of the quadratic
equations within my mathematics internal assessment which explores the relationship
betweenspeedofthesoftballandtimeuntilcontactwiththebat.Duetoerrorswithinmy
datacollectionprocessthereisaquadraticrelationshipbetweenthedatapoints,which
forcestheequationthatisformedtobeaquadraticfunction.Theseerrorsareknownas
human error and can only be fixed if the process is computerized instead, yet these
errors only occur as batters constantly change their positions between pitches to
, maximize their performance and probability of hitting the ball. Thiscausesvariancein
thedatawhichcausesahighercorrelationforthequadraticinsteadofalinearfunction.
However mathematicallythequadraticcannotbecorrectasthegraphbeingplottedis
speed against time which should be portraying a linear relationship. Though
theoretically thefunctionandmodelwasamisrepresentationoftheactualrelationship,
itwasstilluseful.Inthisinstance,thefunctionwillbeintegratedinordertoconfirmthe
area under the curve (in mathematical terms) or totaldistancetravelledbytheball(in
the real life scenario). Even though the model of the quadratic function can be
consideredwrongasitdoesn’tadheretothecorrectmathematicalrelationships,itisstill
usefulasitwillallowmetogettotheintegratedfunctionwhichwillthenbebeneficialin
conducting more calculations to get the final answer. The linear functionmodelwould
still be able to produce a sufficient answer, yet it was not selected due to the lack of
correlation withthedatapointscomparedtothequadraticfunction.Thiscanallowone
to ponder if knowledge can still remain valid even if the model is flawed? However it
appears that in mathematics models are somewhat of a stepping stone for future
theories and functions that can be solved (“When Models Are Wrong, but Useful |
Mathematical Institute”).Fromthisitisevidentthatamodel’susefulnessisnotentirely
dependent on its complete precision.
Nonetheless others may argue that it is possible to come to other conclusions
using mathematical models toconcludethatallmodelsareindeedwrong.Thiscanbe
seenbylookingatmathematicalmodelsastheyallrequireafinitenumberthatcanbe
modelled. Numbers such as infinite decimals and irrational numbers (such as pi) are
I agree to a certain extent with the claim: “all models are wrong, but someare
useful” as this can be seen through the Areas Of Knowledge of Mathematics and
Natural Sciences. Itisessentialtounderstandwhatamodelisasitwillhelpguidethe
discussiononwhetherallmodelsareconsideredwrong.Amodelisgenerallyknownas
a visual representation of a proposed structure to help predict a trend
(Merriam-webster). However models may appear as wrong as they are merely
“approximationsofreality”whichcanlimittheirusage(“AllModelsAreWrong”).Itisalso
importanttoacknowledgethatthisclaimstatesthatallmodelsarewrong,whichmeans
that the whole quantity of models that exist and will further exist in the future are all
incorrect. Fundamentally, it is important to understand how wrong the modelshaveto
be in order to be considered ‘not useful’ (“AllModelsAreWrong”).Tofurtherdiveinto
this question, I will be exploring this through the usage of mathematical models and
biological models.
Mathematics is a great example to demonstrate how models canbewrongbut
useful simultaneously. For example we can analyze the usage of the quadratic
equations within my mathematics internal assessment which explores the relationship
betweenspeedofthesoftballandtimeuntilcontactwiththebat.Duetoerrorswithinmy
datacollectionprocessthereisaquadraticrelationshipbetweenthedatapoints,which
forcestheequationthatisformedtobeaquadraticfunction.Theseerrorsareknownas
human error and can only be fixed if the process is computerized instead, yet these
errors only occur as batters constantly change their positions between pitches to
, maximize their performance and probability of hitting the ball. Thiscausesvariancein
thedatawhichcausesahighercorrelationforthequadraticinsteadofalinearfunction.
However mathematicallythequadraticcannotbecorrectasthegraphbeingplottedis
speed against time which should be portraying a linear relationship. Though
theoretically thefunctionandmodelwasamisrepresentationoftheactualrelationship,
itwasstilluseful.Inthisinstance,thefunctionwillbeintegratedinordertoconfirmthe
area under the curve (in mathematical terms) or totaldistancetravelledbytheball(in
the real life scenario). Even though the model of the quadratic function can be
consideredwrongasitdoesn’tadheretothecorrectmathematicalrelationships,itisstill
usefulasitwillallowmetogettotheintegratedfunctionwhichwillthenbebeneficialin
conducting more calculations to get the final answer. The linear functionmodelwould
still be able to produce a sufficient answer, yet it was not selected due to the lack of
correlation withthedatapointscomparedtothequadraticfunction.Thiscanallowone
to ponder if knowledge can still remain valid even if the model is flawed? However it
appears that in mathematics models are somewhat of a stepping stone for future
theories and functions that can be solved (“When Models Are Wrong, but Useful |
Mathematical Institute”).Fromthisitisevidentthatamodel’susefulnessisnotentirely
dependent on its complete precision.
Nonetheless others may argue that it is possible to come to other conclusions
using mathematical models toconcludethatallmodelsareindeedwrong.Thiscanbe
seenbylookingatmathematicalmodelsastheyallrequireafinitenumberthatcanbe
modelled. Numbers such as infinite decimals and irrational numbers (such as pi) are
