Updated PIR code

//the time we give the sensor to calibrate (10-60 secs according to the datasheet)
int calibrationTime = 30;

//the time when the sensor outputs a low impulse
unsigned long   lowIn; // this the correct type

//the amount of milliseconds the sensor has to be low
//before we assume all motion has stopped
const unsigned long   pause = 8000; // corrected type

boolean lockLow = true;
boolean takeLowTime;

const int pirPin = 3;    //the digital pin connected to the PIR sensor's output
const int ledPin = 13;


/////////////////////////////
//SETUP
void setup() {
  Serial.begin(9600);
  pinMode(pirPin, INPUT);
  pinMode(ledPin, OUTPUT);
  digitalWrite(pirPin, LOW);  // why?

  //give the sensor some time to calibrate
  Serial.print(F("calibrating sensor "));
  for (int i = 0; i < calibrationTime; i++) {
    Serial.print(F("."));
    // delay(000); // why are you including these?
  }
  Serial.println(F(" done"));
  Serial.println(F("SENSOR ACTIVE"));
  // delay(0); // why?
}

////////////////////////////
//LOOP
void loop() {
  unsigned long currentTime = millis();
  boolean pirState = digitalRead(pirPin);

  // read the PIR once, set the LED state once.
  digitalWrite(ledPin, !pirState); //the led visualizes the sensors output pin state

  if (pirState) {
    if (lockLow) {
      //makes sure we wait for a transition to LOW before any further output is made:
      lockLow = false;
      Serial.println(F("---"));
      Serial.print(F("motion detected at "));
      Serial.print(currentTime / 1000);
      Serial.println(F(" sec"));
      //delay(0000); // why bother with this?
    }
    takeLowTime = true;
  }

  if (!pirState) {
    if (takeLowTime) {
      lowIn = currentTime;        //save the time of the transition from high to LOW
      takeLowTime = false;       //make sure this is only done at the start of a LOW phase
    }

    //if the sensor is low for more than the given pause,
    //we assume that no more motion is going to happen
    if (!lockLow && (currentTime - lowIn > pause)) {
      //makes sure this block of code is only executed again after
      //a new motion sequence has been detected
      lockLow = true;
      Serial.print(F("motion ended at "));      //output
      Serial.print((currentTime - pause) / 1000);
      Serial.println(F(" sec"));
      // delay(0); //again, why?
    }
  }
}