Our Gemara on Amud Aleph discusses a certain kind of intuition, whereby there is a sense of foreboding without any known reason. Therefore, even though Haggai, Zechariah, and Malachi did not actually see the vision that Daniel was seeing of a fearsome angelic being in real time, they were still in a state of uncanny dread. The Gemara explains that though they did not see the vision, their “mazal” saw it. Rashi translates this as their ministering angel assigned to the person above. However we understand this, it means that there is a non-conscious perception of a non-physical phenomenon. The Gemara goes on to offer some practical advice:
Ravina said: Learn from this incident that with regard to one who is frightened for no apparent reason, although he does not see anything menacing, his guardian angel sees it, and therefore he should take steps in order to escape the danger. The Gemara asks: What is his remedy? He should recite Shema, which will afford him protection.
There are other scriptural and rabbinic teachings which support the idea that one can have an intuition, and be guided by it.
For example, Iyov (3:25) speaks of having had a premonitory sense that some calamity would befall him:
כִּ֤י פַ֣חַד פָּ֭חַדְתִּי וַיֶּאֱתָיֵ֑נִי וַאֲשֶׁ֥ר יָ֝גֹ֗רְתִּי יָ֣בֹא לִֽי׃
I had no repose, no quiet, no rest, and trouble came.
Malbim and Chida (Chomas Anakh) note that Iyov had a sixth sense, coming from his mazal, that something terrible would happen. The Chida (Penei Dovid Shemos 1:10) also suggests that even Pharaoh had an intuition that Egypt would be drained and emptied of its wealth by the Jews abruptly leaving, which is why he enslaved them in the first place, rationalizing: “Let us deal shrewdly with them, so that they may not increase; otherwise in the event of war they may join our enemies in fighting against us and rise from the ground.”
Pele Yoetz (Tahara) says that should a person feel an unusual arousal for either joy or sadness, he should capitalize on it through intense service to God, as the feeling dictates. He states the emotions are being influenced by a sense of something significant occurring in relation to him in the spiritual domain. Likewise, Likkutei Moharan (118:1) offers advice on how to be mobilized by these intuitions:
Know! It sometimes happens that a decree is issued against a person, God forbid, which, although he might not see, his guardian angel sees (Megillah 3a). For this reason he wants to hide himself. This is why, occasionally, a person will travel suddenly to someplace distant. This is in order to hide himself. And although he is unaware of this, even so, his soul is aware of this. Therefore, he gets an urge to travel there.
Presumably, the change in location will change the mazal, and perhaps humble the person to repent as well.
He states further (4:9)
This is why we see that now and then a person becomes inspired while praying and he recites several words with tremendous fervor. This is due to God’s compassion for him; the Light of Ein Sof has been opened to him and shines for him. When a person sees this radiance—and even though he might not see, his mazal sees (Megillah 3a) —his soul is instantly ignited in great devotion, so that he attaches himself to the Light of Ein Sof. And, to the degree that Ein Sof is revealed—commensurate with the number of words that have been opened and begun to radiate—he recites all these words with great devotion, with a surrender of self, and with a negation of all his senses. Then, during the time he is negated in Ein Sof, he is in a state of “and no man knows,” so that he himself is unaware of his own existence. But this must be in the aspect of fleeting in order to preserve his soul within him, and he not become completely absorbed and merged into the spiritual realm.
Another example comes from the Arizal אורח חיים תקפ״ד באר היטב ג he states that if a someone feels during the Days of Awe a spontaneous, overwhelming urge to cry greatly, he is being judged at that moment in the heavenly court.
(We discussed other ways to capitalize on the energy of certain intuitive insights in psychology of the daf Taanis 29.)
It is important to study the phenomenon of intuition from a psychological and spiritual perspective, as this is an area that is greatly neglected in our modern world. With the advent of the modern scientific and rational age, there is an increasing amount of contempt for so-called irrational thoughts and beliefs. Scientific reasoning has allowed us to make great advances by freeing us from shackles of arbitrary superstitious beliefs and mythological thinking. This has led to revolutions in science and even government because the rule of law and intellectual discourse became more based on rational ideas and natural self-evident concepts, instead of capricious leaders holding onto power and beliefs that are rigid and not respectful of true human nature.
Yet, slavish worship of the scientific method also has led to a denigration of symbolic and intuitive perceptions. Such perceptions may not be empirically provable but they aren’t irrational either. Something that is irrational is not the same as non-rational. Irrational has an implication that it does not make sense and is even lacking in sanity. Non-rational just means it operates in a context that cannot be logically measured or reasoned. Mother’s love is non-rational but certainly not irrational. We cannot quantify or explain what mothers love is, nor can we substitute it with chemicals. Even if one day we were able to create the right Neurochemical responses that come about when one experiences mother’s love, that would not in any way describe the subjective personal human experience. For example, I can be a computer programmer, and know how to program a beautiful song so that a computer plays it. I could have it calculated down to the last note and meter. At the same time, the only time I really will enjoy that musical piece is if I listen to it. Knowing how it works, and even somehow constructing it, is in no way a substitute for the superiority of the experience. Many spiritual and emotional ideas can be grasped non-rationally and intuitively. If we overdo being rational, we miss out on a source of data that is vital, even if hard to quantify. You might just know your son “needs” a ride to school today even though logically he can take the bus. Or you might just “know” how much salary to ask for on a job interview, or which employee is a better fit for a job, without any hard data.
How do we define intuition? According to researcher Seymour Epstein ( Reference: Epstein, S. (2010). “Demystifying Intuition: What it is, what it does, and how it does it.” Psychological Inquiry, 21, 295-312. ), there are as many as 20 psychological definitions for intuition. He attempts to define intuition as follows:
It is a form of information processing that is different from analytical reasoning. According to Hogarth (2001) “the essence of intuition or intuitive responses is that they are reached with little apparent effort, and typically without conscious awareness. They involve little or no conscious deliberation” Epstein concludes, iIntuition involves a sense of knowing without knowing how one knows. Intuition involves a sense of knowing based on unconscious information processing.
Epstein goes on to explain how humans can be understood as operating in two realms simultaneously. According to cognitive-experiential self theory (CEST) humans operate with two information-processing systems, an experiential system, which is an automatic, associative learning system ,and a rational/analytic system, which is a verbal reasoning system. The systems operate by different rules and have different attributes. …The content of the experiential/intuitive system consists primarily of generalizations from experience, and its major motive is to behave according to the hedonic principle, i.e., to pursue positive affect and avoid negative affect. This makes the experiential system an affect-driven cognitive system.
In contrast to the outcome-orientation of the experiential system, the rational system is a verbal reasoning system that operates according to a person’s understanding of logical inference. The system operates in a manner that is conscious, abstract, analytic, affect-free, effortful, and highly demanding of cognitive resources. It acquires its beliefs by logical inference.
On the positive side, the rational system is the source of humankind’s remarkable accomplishments. It is able to think at high and complex levels of abstraction with the aid of verbal symbols and to accumulate knowledge across cultures and generations through written language. It is capable of understanding cause and effect relations, of planning for the future, of applying broad abstract principles across situations, and of taking long-term consideration into account. On the basis of such thinking it has been the source of humankind’s remarkable achievements in science, technology, mathematics, medicine, and other disciplines, that no other species comes close to emulating.
On the negative side, the rational system is too effortful and slow for efficiently directing everyday behavior. People do not deliberate over their everyday behavior, they simply behave. A further limitation of the rational system is that it is an affect-free verbal reasoning system. Its lack of affect-driven motivation leaves it with its only direct source of motivation being cognitions about how one should behave, which may be a weak and easily biased source of influence when in conflict with strong, emotion-based motives in the experiential system.
An example of this is the occurrence of phobias. People may desperately wish to get rid of them to no avail. Will-power in the domain of the rational system), is rarely up to the task of vanquishing phobias. In psychotherapy, people often find that intellectual insight makes little difference but that what is successful is the use of procedures that produce changes in the experiential system, as in systematic desensitization, which is a de-conditioning procedure.
The strengths of the experiential/intuitive system are that it rapidly and effortlessly directs everyday behavior, it is a source of affect-driven compelling motivation, it can establish a sufficiently accurate model of the environment that allows for effective adaptation to the environment by empirically learning from experience, it provides an alternative source of decision-making that is sometimes more effective than decisions made by deliberative reasoning, and by relying on “multiple fallible indicators” it can avoid the catastrophic consequences that can occur from small errors in linear-reasoning (Brunswik, 1956; Hammond, 1996)…In addition, an experiential/thinking style is associated with favorable interpersonal relationships, social popularity, agreeableness, empathy, spontaneity, emotional expressiveness, a good sense of esthetics, a good sense of humor, creativity, open-mindedness, and personal growth.
On the negative side, although the experiential/intuitive system could, by itself, sustain life, it would do so in a manner that would fall far short of providing normal human behavior. Also, an experiential/intuitive thinking style, if uncorrected by the rational/analytic system, tends to be associated with naïve optimism, Polyannaish thinking, stereotyped thinking, unusual and unrealistic beliefs, and superstitious beliefs.
Epstein is explaining, in a structured style, the duality of human personality that sages and philosophers have grappled with for millenia. The heart versus the mind, the spiritual versus the rational, and even the conscious analytical part of the mind, versus the unconscious symbolic, instinctive part of the mind. A healthy organism is able to integrate information from both sources and maintain a healthy balance between both states. Basically, listen and be mindful of your instincts, emotions and intuitions, but don’t always obey them.
Translations Courtesy of Sefaria, except when, sometimes, I disagree with the translation 
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