A number form is a mental map of number

Number

A number is a mathematical object used to count and measure. In mathematics, the definition of number has been extended over the years to include such numbers as zero, negative numbers, rational numbers, irrational numbers, and complex numbers....

s, which automatically

Automaticity

Automaticity is the ability to do things without occupying the mind with the low-level details required, allowing it to become an automatic response pattern or habit. It is usually the result of learning, repetition, and practice....

 and involuntarily appears whenever someone who experiences number-forms thinks of numbers. Numbers are mapped into distinct spatial locations and the mapping may be different across individuals. Number forms were first documented and named by Sir Francis Galton

Francis Galton

Sir Francis Galton /ˈfrɑːnsɪs ˈgɔːltn̩/ FRS , cousin of Douglas Strutt Galton, half-cousin of Charles Darwin, was an English Victorian polymath: anthropologist, eugenicist, tropical explorer, geographer, inventor, meteorologist, proto-geneticist, psychometrician, and statistician...

 in his The Visions of Sane Persons . Later research has identified them as a type of synesthesia

Synesthesia

Synesthesia , from the ancient Greek , "together," and , "sensation," is a neurologically based condition in which stimulation of one sensory or cognitive pathway leads to automatic, involuntary experiences in a second sensory or cognitive pathway...

 .

Neural Mechanisms

It has been suggested that number-forms are a result of "cross-activation" between regions of the parietal lobe

Parietal lobe

The parietal lobe is a part of the Brain positioned above the occipital lobe and behind the frontal lobe.The parietal lobe integrates sensory information from different modalities, particularly determining spatial sense and navigation. For example, it comprises somatosensory cortex and the...

 that are involved in numerical cognition

Numerical cognition

Numerical cognition is a subdiscipline of cognitive science that studies the cognitive, developmental and neural bases of numbers and mathematics. As with many cognitive science endeavors, this is a highly interdisciplinary topic, and includes researchers in cognitive psychology, developmental...

 and angular gyrus for spatial cognition . Since the areas that process numerical and spatial representations are close to each other, this may contribute to the increased cross-activation. Compared to non-synesthetes, synesthetes display larger P3b amplitudes for month cues, but similar N1 and P3b responses for arrow (<- or ->) and word (left or right) cues. .

Reaction Times

Reaction time studies have shown that number-form synesthetes are faster to say which of two numbers is larger when the numbers are arranged in a manner consistent with their number-form, suggesting that number forms are automatically evoked . This can be thought of as a "spatial Stroop

Stroop effect

Purple Blue Purple----Blue Purple RedGreen Purple Green----the Stroop effect refers to the fact that naming the color of the first set of words is easier and quicker than the second....

" task, in which space is not relevant to the task, but which can hinder performance despite its irrelevance. The fact that synesthetes cannot ignore the spatial arrangement of the numbers on the screen demonstrates that numbers are automatically evoking spatial cues.
The reaction times for valid cues are smaller than invalid cues (words and arrows), but in synesthetes the response time differences for months are larger than those of non-synesthetes .

Difference between number line

These number forms can be distinguished from the non-conscious mental number line

Number line

In basic mathematics, a number line is a picture of a straight line on which every point is assumed to correspond to a real number and every real number to a point. Often the integers are shown as specially-marked points evenly spaced on the line...

 that we all have by the fact that they are 1) conscious, 2) idiosyncratic (see image) and 3) stable across the lifespan. Although this form of synesthesia has not been as intensively studied as grapheme-color synesthesia

Grapheme-color synesthesia

Grapheme → color synesthesia is a form of synesthesia in which an individual's perception of numbers and letters is associated with the experience of colors. Like all forms of synesthesia, grapheme → color synesthesia is involuntary, consistent, and memorable...

, it seems reasonable to assume that similar neural mechanisms might be involved, but acting in different brain regions. Future studies will need to be conducted to test this hypothesis.