Tag Archives: meaning

Logic and Math

So here we have a brain whose association cortex works overtime to combine sensory information into a stream of relationships in space and time. In fact, you cannot shut off this process or stop the brain from constantly searching its sensory inputs for patterns, even when there are no patterns to be found!

The time domain is particularly interesting because it is here that we build up the ideas of cause-and-effect and create various rules-of-thumb that help us predict the future, find food, and many other activities. This specific rule-type association largely takes place in the dominant hemisphere of the brain (left side for right-handed people) which also has the speech center. Specifically, the frontal lobes are generally considered to be the logic and reasoning centers of the brain. So when the brain is talking to you, it also has easy access to logical tools of thinking. We also have a minor hemisphere (right-side for right-handed people) that specializes in pattern recognition, but it contains no language centers and is therefore mute. Its insights about the patterns that it finds in sensory data are totally overtaken by the constantly babbling left-hemisphere. All it can muster is that non-verbal feeling of ‘Eureka!’ you get  once in a while.


This sequence of brain scans shows the four stages of math problem solving from left to right: encoding (downloading), planning (strategizing), solving (performing the math), and responding (typing out an answer).

Anyway, brain researchers have done brain imaging studies to explore where math reasoning occurs. They found that, when mathematicians think about advanced concepts, the prefrontal, parietal, and inferior temporal regions of the brain become very active. But this activity didn’t also happen in brain regions linked to words. This means, as many mathematicians can tell you, mathematics is not related to the brain’s language centers. It is an entirely different way of communication. In other words, you can carry-out mathematical thinking without an internal voice speaking. It is an entirely non-verbal activity until you are interested in communicating your results to someone else. I know this myself when I am solving complex equations. Not a single conscious word is involved. Instead, I move my hands, squirm in my chair, and robotically step through the methods of solving the equations without any verbal prattle like ‘Ok…this goes over here and that goes down here and x moves to the other side of the equals sign’ …and so on. I keep telling the public that math is the language of science, but in fact it is not really a language at all. It’s like saying that oil is the language of painting a work of art! In fact, when you are proficient at mathematics, you are behaving like a concert violinist who does not think about each note she plays, but flows along on a trained sequence of steps that she learned. Her sequence of fine motor skills are stored in the cerebellum, but a mathematician’s skills are stored in an entirely different part of the brain.

Researchers have found a group of a few million cells located in a region called the inferior temporal gyrus. These cells seem to respond very strongly when you are doing concrete, numerical calculations like balancing your bank account, filling out your taxes, or plugging-in numbers in a complex equation to get an answer . So the brain does have discrete regions and clumps of neutrons that make mathematical reasoning possible. An entire hemisphere is dedicated to ‘logical analysis’, but specific locations allow you to work with this implicit logic in an entirely symbolic manner that resembles the language centers in the Broca’s and Wernicke areas, which facilitate speech and writing words.

So here we now have all the elements for creating a model of the outside world by using sensory data to find patterns in time, and to use these patterns to eventually deduce general mathematical If A then B logical statements about them that are entirely symbolic, and far more accurate than what the brain’s language centers can provide through its endless chatter.

The basis for all these deductions about the world outside the brain is a concrete understanding of what space and time are all about. We learn about space through our binocular vision, but also because our mobility allows us to move through space. Even with perfect stereo vision, you have no idea what those objects are that you are looking at unless you can literally walk over to them and appreciate their actual sizes, textures and other features. So our deep, personal understanding of 3-dimensional space comes about because we have mobility and stereo vision. But actual vision as a sense may not be that important after all. Echolocation used by bats and dolphins is not a visual decomposition of the world but an auditory one, processed to give back a 3-dimensional model of the world without vision, color or even the perception of black and white being involved.

Evidence from  brain-imaging experiments indicates that, when blind people read Braille using touch, the sensory data is being sent to, and processed in, the visual cortex. Using touch, they get a sense of space and the relative locations of the raised dots that form Braille letters . Although the information is processed in the visual cortex, their impression is not a visual,  but is instead a directly spatial one without the intermediary of vision to get them there!

Next time I will begin the discussion about how astronomers and physicists ‘envision’ space itself.

Check back here on Monday, December 12 for the next installment!

Mathematical Ability Revealed in Brain Scans, 2016, By Mindy Weisberger

Other related essays:
Your Brain on Math

How Do Blind People Picture Reality? By Natalie Wolchover


There are at least two basic ways that we create associations. The first is associations in space. The second is associations in time.

Associations in space include recognizing static objects like chairs, trees, cars and people. The reason this works so well is that we live in a world filled with many different kinds of more-or-less fixed objects so that two or more people can agree they have similar attributes.

Associations in time include musical tunes and sounds, or associating one thing (cause) with another thing in the future (effect). For many of these dynamic associations like music, two people with normal hearing senses hear the same sequence of notes in time and can agree that what they heard was a portion of a familiar song, which they may independently be able to name if they have heard it before and made the appropriate associations in memory. But your exact associations related to the song will be different than mine because I associate songs with episodes in my life that you do not also share. Remember, the brain tags everything with patterns of associations unique to the individual.

The human brain is adept at pattern recognition. It can dissect its sensory information and see patterns in space and time that it can then associate with abstract categories such as a chair or a bird, and even specific sub-categories of these if it has been adequately trained (at school, or by reading a book on ornithology!). An upside-down chair seen in the remote distance is recognized as a chair no matter what its orientation in the visual field. A garbled song heard on an iPhone in a loud concert hall, or a particular conversation between two people in a noisy crowd, can also be detected as a pattern in time and recognized. The figure shows some of the brain connection pathways identified in the Human Connectome Project that help to interpret sensory data as patterns in space and time.


Patterns in space let us recognize the many different kinds of objects that fill our world. In the association cortex, once these identifications have been made, they are also sent on to the language centers where they are tagged with words that can be spoken or read. Once this step happens, two individuals can have a meaningful conversation about the world beyond their bodies that the senses can detect. Of course when both people say they have a specific category of objects called Siamese cats, they are most certainly associating that name with slightly different set of events and qualities corresponding to their cat’s personalities , fur patterns, etc..

The next step is even more interesting.

Just as the brain generalizes a collection of associations in space to define the concept of ‘cat’, it can detect patterns in time in the outside world and begin to see how one event leads to another as a rule-of-thumb or a law of nature. If I drop a stone off a tall cliff, it will fall downwards to the valley below. If the sun rises and sets today, it will do so again tomorrow. There are many such patterns of events in time that reoccur with such regularity that they form their own category-in-time much as ‘cat’ and ‘chair’ did in the space context. ‘If I visit a waterhole with lots of animals, there is a good chance that tigers or lions may also be present’. More recently, ‘If I stick my finger in an unprotected electrical outlet, I will probably be electrocuted!’. This perception of relationships is one of cause-and-effect. It has been studied by neurophysiologists, and is due to stimulation of part of the cerebellum and the right hippocampus. These brain regions are both involved with processing durations in time.

Over the centuries and millennia, the patterns in time we have been able to discern about the outside world have become so numerous  we have to write them down in books, and also put our children through longer and longer training periods to master them. This also tells us something very basic about our world.

Instead of being a random collection of events, our physical world contains a basic collection of rules that follow a ‘logical’ If A happens then B happens pattern in time. Physicists call these relationships ‘laws’ and their particular patterns in time and space can be discerned from measurements and observations made of phenomena in the world outside our brains. The brain can also work with these laws symbolically and logically, not by describing them through the usual language centers of the brain, but through a parallel set of centers that make us adept at mathematical reasoning.

In my next blog, I will discuss how mathematics and logic are intertwined and help us think symbolically about our world.

Check back here on Friday, December 9 for the next installment!

Space, Time, and Causality in the Human Brain

What does it mean?

What happens to all this sensory information that gives you a concrete idea about the things that exist in your world?

We saw how the flow of sensory information at any one time is enormous. It starts out as separate streams of information that flow to specific brain regions as their first stop, but then after that the information radiates to many different regions in the brain where it gets mixed with our emotions, and even with other sensory information. This is a process that is called association, and a large volume of the brain is called the Association Cortex for that reason.


At first the auditory information called purring, is connected to other sensory information occurring at the same time, for instance, the feeling that something furry is brushing against your leg. These two pieces of information become associated with each other, especially if they are connected to a similar combination you experienced earlier, and which was associated in your language cortex as the sound of the word ‘cat’ or the written word ‘cat’. Communicating this information is then handled by Broca’s Area (speech generation ) and Wernicke’s Area (speech comprehension).

The brain creates meaning by associating sensory information with specific categories of past experience. Nothing can really be understood except through a complex process of being associated with other things you have experienced, or learned. It’s like some enormous, interlinked tapestry of connections, and adding a new bit of information is always about fitting it into what has already been experienced in some way. But if that were all that there is, we would simply be walking encyclopedias.

Most of us have senses that are pretty well-defined. For example, the optic nerve transmits what each eye’s retinas detect and passes this on to the visual cortex at the back of the head after some of this information is first linked by neurons to a small brain region called the suprachiasmatic nucleus and then on to the pineal gland (to detect the day-night cycle). It also connects with the thalamus where it gets associated with other sensory stimuli. The three types of retinal cone cells are tuned to slightly different wavelengths of light and send the usual neural signals along the optic nerve. The outside world actually has no color at all. Everything is decided by the wavelength of light, and this number does not include color information. But by the time the visual cortex and its related association cortex is finished processing the information from the cones, you have a definite internal sense of color being an intimate part of the world. This is, however, very different than seeing the world in black and white, which is actually a better representation of what the world looks like. Our retina also have rod cells that are very sensitive to light intensity at all visual wavelengths, but give you only a sense of a grey world!

By coding light frequency information as well as intensity, our eyes and brains over eons of evolution have ‘decided’ that this extra color information has survival value. It can help classify things in terms of specific frequency fingerprints. For example, a coral snake is deadly and a scarlet king snake is harmless. Their skins have yellow and red bands, and the rhyme ‘Red touch yellow, kills a fellow but red touch black is a friend of Jack’ helps you distinguish between the two. You would be dead if all you could see is black and white. In fact, the complex color selections seen in nature have actually co-evolved with color vision over millions of years. The scarlet king snake adapted a version of the color coding used by coral snakes to fool predators into thinking it was a poisonous snake!

Sometimes this process can be flawed. We all know about color blindness, which affects about 8% of men and 0.5% of women. This happens when one of the three cone cell populations in the retina do not work properly. There is no way for the brain to correct for this because the retina has eliminated an important color sense long before the information reaches the optic nerve and the visual cortex.
There is another sensory malady that is even more unusual. Called synesthesia, it is caused by synaptic connections between otherwise separate sensory channels. For instance, you might see letters of the alphabet as having distinct colors on the page, or associate a specific sound with a color, among dozens of other documented possibilities. It is actually much more common than you might suspect. Have you ever felt that numbers have a definite location in space, or that 1980 is ‘farther away’ than 1990? Studies of the brain show that these mixings happen because of cross-wiring of neurons in the brain, either due to genetics or due to training when you were very young.

So, it isn’t even true that everyone perceives the outside world in identical manners. This leads to differences in how each person categorizes events and their internal associations with other things we have experienced. So with all of these variations in exactly what a ‘cat’ is, how do we create models of the world that let us function and survive without having accidents and getting killed all the time?

In my next blog I will describe two very unusual, personal experiences that show how our experience of the world can be temporarily distorted.

Check back here on Monday, December 5 for the next installment!
Seeing Color: http://www.webexhibits.org/causesofcolor/1C.html