I would make a hypothesis as simple as possible to understand and remember.  So I can say, 'Loss of heat is proportional to decrease in temperature', to represent HEAT LOSS= mc (temperature drop); where m is mass and c is specific heat capacity.

(The hypothesis must focus on something that can be tested, and includes an independent variable and a dependent variable.  But is there a need to have the same words expressed in the same order?  If so stating it in it's briefest form will meet that goal, perhaps.)

Perhaps hypothesis-presentation in scientific publications should follow rules as applied in Taxonomy. One person defines a hypothesis for the first time to be replicated in exactly the same way in subsequent publications dealing with the same hypothesis.

Perhaps people could construct 'taxonomy-type trees' for each class of hypotheses, starting with an ancestor hypothesis that subsequently is subdivided into different types of hypothesis-presentation. The hypothesis-presentation (e.g. number and order of words used) within a given language will probably depend on the education background of authors involved. The education background of an author of a scientific publication might be defined as a selection pressure favouring or excluding a given hypothesis-presentation.

The chances of the thousand researchers having the same training in English is estimated (by little me!) as p=0.1. The chances of the researchers having the same training, background and research approach is (I guess again!) p=0.01. So, given one researcher's statement of the hypothesis, there might just be one other researcher who has the identical statement of the hypothesis.

I know of one case where two research groups worked independently on the same topic and each submitted papers with the identical title! (By a quirk of fate, both papers were accepted!).

Especially in English, because we have stolen so shamelessly from other languages, we have many synonyms. In developing our paper on queueing, I had tremendous difficulty in finding prior art, especially as it has application to so many fields of endeavour, each with their own different terminology. My co-author helped by showing a whole discipline that used different terminology. Conversely, I had difficulty in choosing a title for our paper that could be Googled by researchers in different fields.

There is no expectation that two authors will use the same word in the same order. This is what makes Googleing in Scholar such fun. You have to try hard to anticipate conceivable synonyms. This is an art and not a science.

The fun continues when you try to bring together all the threads in the critical review of the literature with a unified vocabulary and terminology. Do you use the vocabulary of the first author? The vocabulary of the busiest field? The most recent? Or, invent your own, unifying terminology?

Each of our research authors are entitled to use (and should use) the words that they believe best express what they have done and found. Standard advice to research writers is to keep to one set of terminology in one paper. Rare is the advice to research writers to initially seed the paper with all possible synonyms, so that their papers can be found by all audiences from all fields. Researchers need to be aware of the techniques of Search Engine Optimisation as a tool for the widespread dissemination of their research work.

Hello Ian,

If one would compare 'Mathematical language' with other 'human-created languages' (e.g. English or a dialect), I would say there is more liberty in the expression of the 'non-Math languages' when different workers focus on the same phenomenon, and this because of many reasons as you indicate.

Germanic languages have less variability and should be better for scientific correspondence than English. However, there is still the problem of which school you went to and which school of thought they belong to!

In our case, (M/M/r/K/K queue), even the symbols are not standardised beyond the first two! Pick a letter from a to Z, and if you are not happy with one of those, borrow from the Greeks!

Of course. Imagine all the local dialects that exist and consequences for local education (private-mother versus public-teacher education environments)!

I would make a hypothesis as simple as possible to understand and remember.  So I can say, 'Loss of heat is proportional to decrease in temperature', to represent HEAT LOSS= mc (temperature drop); where m is mass and c is specific heat capacity.

(The hypothesis must focus on something that can be tested, and includes an independent variable and a dependent variable.  But is there a need to have the same words expressed in the same order?  If so stating it in it's briefest form will meet that goal, perhaps.)

But what about natural history hypotheses, for instance? Birds sing because.....

@Sergei: Not specific enough, I think. Open to different interpretations and results?

The best hypotheses minimize the number of results supporting it, or not?

For  hypothesis formulation and testing, you may look at the following link:

http://www.investopedia.com/exam-guide/cfa-level-1/quantitative-methods/hypothesis-testing.asp

Dear Sergei,

I will depend on what bird species you are studying. Birds can be found in different habitat types, including forest habitat.  Perhaps concerning the microbiome you mention, a host could also be subdivided into different habitat types, or not? Different microbiomes on different places in/on the host?

Why we should be interested in such questions. It is well known that any observer  has its own subjectivity. But finally the hypothesis they make will be judged in practice! So make whatever hypothesis you like, express it in any words you like. Finally if published then it will constitute a original contribution to science, if not nobody is harmed!

It is not so immediate to produce an answer. The difficulty comes from the occurrence that you are proposing a question about a scientific hypthesis (i.e an hypothesis within a formal construct) adopting every day language. The adoption of every day language immediately face us with a sort of ambiguity.

I will try to explain. Your question start depicting a situation: "1000 people observe the same phenomenon 'C'. What really means this sentence? Literally you are stating that a phenomenon is occurring. As an example, an apple is falling down from a three. There are 1000 people which are present at the same time and in the same place. And each of them is observing the same apple falling down from the same tree, at the same time and in the same place. For sure, this is literally the meaning of your question. But I cannot imagine that no one among the 1000 people would be able to hypothesize nothing of reasonable, if the described event is unique, i.e. if this was the first time that each of them is observing something falling down. So in such a case my answer would be: I think it is hugely improbable that two people among the 1000 will formulate the same hypothesis able to produce a rationalization of the event "the apple is falling down".

But I do not believe that your question must be taken so literally! I am tryed to guess that the word "same" in your question must be interpreted as "similar". But, even with such an interpretation, a sort of ambiguity survives. I can imagine that each one among the 1000, is observing a different apple falling down from a different tree at different places and different times. However, if for each of them this is the first time that an apple falling down from a three is observed, the situation does not look to me different from the previous one. So my answer would be the same.

So, I have to attempt a further interpretation of the situation described in your answer. The new interpretation is: each people is observing his own apple falling dawn from his local three. But each of them has been informed about the observations from the other 999. This makes the situation different. Now, each of them can try to produce a ganeralization. In doing this each of them can make an hypothesis able to explain why an apple can fall down from a three. If I assume that no one of them have ever observed any object falling down, and if I assume that each of them has the same basis of knowledge, than I can imagine that there is some probability that two of them produce similar hypothesis. But the hypothesis will concern just with apples and threes!

A further possible interpretation is: each one among the 1000 is observing an arbitrary object falling down from an arbitrary height, and each one knows what the other 999 observed. Now, each of them can really produce a true generalization. The common observation is no more the observation of the single object falling down. The word "observation" now is indicating the full knowledge that the 1000 shared among them: 1000 objects fell down from different heights. Now it is probable that sever people can imagine the same explanation able to explain why, everywhere through the world, objects can fall down. The explanation will involve the formulation of an hypothesis. But there are several possible hypothesis. One can imagine that a force exists which attracts the objects towards the earth. But one other can imagine that the objects fall down because their natural position is "at the mimum possible height": this would be an aristotelian point of view, which at this level is not worst than any other. And many othe possible hypothesis can exist. However, among the 1000 it is now possible that few peoples can imagine similar hypothesis. If we assume that the 1000 people have the same cultural background, the probability that similat hypothesis are produced becomes large.

This is a partial answer to my final interpretation of your question (not to you question!). It is partial because your question was not about similar hypothesis, but about exactly the same hypothesis expressed, within a given language, by exactly the same words.

Once more, we have to decide what we are talking about. As an exaple, if we are talking about a physical hypothesis, we have to take into account that we are faced with a science which usially adopts a rigorous fornal language, Mathematics. So, if the hypothesis formulated is of the kind "the speed of light is a constant", which is the immediate translation in the spoken langauge of the equation "c=const.", than the probability the two people produce the same translation becomes huge. It the hypothesis is expressed by a more complicate equation, or, in a worst situation, by a sequence of complicate equations, the probability of two identical translations reduces drastically, even if never will go to zero.

Bur if we are talking about a science which is not formalized into mathematics the situation becomes much more complicated, There is no formal language shared among peoples speaking different languages. So the only language is the spoken language. We can try to give words specific meanings, in an attempt of avoiding ambiguity, but some ambiguities will survives. I means, if we are talking, as an example, about an hypothesys of the kind of the Darwins selection of species, it is improbable that two different people express it by exactely the same sequence of words. It can be worst, the same sequence of words can be interpreted differently by different people, and this is clear form the fact that Darwin was often misunderstood. It can happen the reverse too. Two different people can produce apparently the same sentence, even if their meanings are not exactly the same.

In summary, In talking about sentences expressed in spoken languages care must be taken in talking about their meaning. The meaning stayes not only in the sentence but in its interpretation. And the situation is very complicated because there is a double interpretation. The first one comes from the proponent that, in producing the sentence, adopts his own interpretation of the words (and adopts his own mental images and analogies), the second interpretation comes from the reader or the listener (which gives his own contribution to produce his final interpretation). 

Concluding this long post, my meaning is that spoken language should be avoided in scientific publications. At the same time, I am conscious that in several situations a formal language to be adopted does not exists. In such a case, different sentences are produced in order to express the same meaning. You, apparently would say "exactly the same meaning". I propose you a new question. How can you be sure that two different sentences are expressing exactly the same meaning? The two sentences are not the same! They become the same after your interpretation. How can you be sure about the objectivity of your interpretation?

However, this can be not a practical limitations. As the time goes on, a sort of general interpretation will emerge. An interpretation will be borrn which will become a shared interpretation. But this will not hinder that one day a further guy will give is your own interpretation to the same sentence. And it can happen that the new interpretation appears as a better interpretation. The old sentence remains the same but with a different meaning. This can be fine! It is ambiguous but without ambiguity how creativity can existi!

Marcel,

if the situation produces a positive answer to your question:

"Also accepting that the same word can have different meanings in a dictionary?"

this would mean that the hypothesis is not well stated! What else? I assumed that in proposing the hypothesis the proponent is making his best to avoid such a sort of trivial ambiguity. I am asserting a different thing. Even after any attempt for avoiding such a sort of trivial ambiguity, some ambiguities will survive. At least if the hypothesis is not so simple as "the speed of light is a constant".

"Two apples on the same tree will always differ physically, depending on the scale of analysis, so can they always be combined in a single class to formulate a hypothesis about the physical behavior of apples ?"

Really not! If the situation is that you literally describe, the answer is not. The apples you observed does not allow you for confirming that you are observing a behaviour which belong to the wide class of the "apples". Your observation is limited to a subset of the class "apples", namely the sub-set "the apple falling down from this specific tree". To be more clear, fhis is the reason for which an experiment must be repeated in different laboratories by different experimentalists before one is allowed for the formulation of an hypothesis of general validity.

Dear Francesco,

I fully agree that pseudo replication may result from hypothesis presentation not taking the scale of data sampling into account. 

Marcel wrote

"Mathematicians add physical phenomena with perceived shared characteristics (1 + 1 = 2). However, two physical phenomena always differ in at least one level of analysis or perception (1' representing phenomenon A does not equal 1'' representing phenomenon B) and phenomena differing in Physics are given the same mathematical weight. Consequently, 1' + 1'' does not equal 2, or 1 + 1 = 2 does not reflect Physics in nature."

This sentence is not correct, or I misundesrtood it.

I will try to explain. Mathematics define the + operation. Mathematics does not tell nothing about the sum rule to be applied to a perceived phenomenon. Two simple exaples. I put a weight M1 on a scale. The scale tell me: the weight of your body is M1. Now I add a second weight, M2, on the scale. The scale tell me: the combined weight of your items is M1+M2. This tell me that addition is a mathematical rule that can be applied to masses. I can use the symbol + for describing the combination of different mass. 

Now I take 1 litre of water. I put my thermometer within water. The thermometer tell me: the temperature of water is 20°C. I put a different container with another litre of water. I put my thermometer within this water. The thermometer tell me: the temperature of the two water is 40°C. Now, I mix the content of the two container. I put the thermomiter in the mixed water. The thermometer tell me: the temperature of water is 30°C. The thermometer told me that combining temperatures is a process which is not conform to the mathemtical sum. Temperature combination implies a different operation which is related with averages. Average can be expressed mathematically. I means Mathematics contains an operation which is conform to the physical combination of temperatures. If you try to combine temperatures by the mathematical operation +, this is a your fault nor a fault of Mathematics. Mathematics produces a number of different combination rules. It is a your task to select the proper rule. And there is no ambiguity. Only one of the mathematical rules will be conform with your measurements.

Marcel,

I try to undestand the meaning of this sentence:

"If each individual is unique in physical structure, quantities exceeding '1' are philosophically not required. In other words, the simplest mathematical based summary of nature's complexity would be '1', and the types of '1' to be mathematically defined would match the number of physical structures investigated."

Once more, I will try to interpret your meaning.

I understood that you are talking about a situation in which any observed object is unique.

If I understtod correctly, under such circumstances, any hypothesis will be an hypothesys concernig the unique object. To be clear: if I have N objects, than I will have N hypotheses.

If this is your meaning, I can see that this situation is possible. But this situation has nothing to do with scientific hypotheses. If I have N objects and N hypotheses, than the hypotheses are producing a catalogue, not a scientific rationalization. To distinguish different objects by their names or by the associated unique hypotheses is formally the same thing. I can substitute names with hypotheses and nothing changes. A scientific hypothesis implyes a generalization. Science implyes generalization. The eplicative content od Science stayes in generalization. To produce a scientific hypothesis I have to understand what different objects have in common. When I see that N objects fullfill my hypothesis, I will check if a further similar object will fullfill my hypothesis. And so on, until the hypothesis will be fasified (if it will happen). The sentence "Science has an explicative content" is not ambigue. It can be formalized. It means that in order to describe my N objects I need to introduce a number of hypotheses n, where n

Mathematic does not make any interpretation at all! Mathematics is a formal system, nothing more. Starting from few axioms it produces a sequence of sentences (theorems or formulas) which are correct. Correct only means that can be derived by a sequence of allowed operations starting from axioms. Which means that, in this contest, the words "correct" and "true" have exactly the same meaning. After this, we can observe some sort of correspondence between the symmetry of our formula and a symmetry observed in Nature. To say that a phenomenon is explained by our formula simply means that we have put into evidence such a kind of apparent symmetry. There is no interpretative step in such a procedure. Mathematics does not produce any interpretation nor any explanation of the real world. Simply tell us how the real world apparently is ruled. Which is a good thing, because allows us for accurate forecasts. Interpretation comes later. We produce interpretation of the mathematical formulas. And such interpretation cannot be ever unique. It is not unusual that there are debats about the meaning of hypotheses and theories.

And you can see that this debats have nothing to do with Mathematics. It is not unusual the theories (and the hypotheses on which they are stated) produce fine forecasts. In spite of the debats about their meaning. Which means that Mathematics works alone, without any need for interpretation.

I definitely disagree. 1+1=2 is not an interpretation at all. It is a formalization, which is a different thing.

To obtain such a kind of relation, with reference with a given measurable propertiy shared by two different items, we are simply observing that the effect of combining the two quantities has the same symmetry of the mathematical sum operation (as an example: A+B=B+A and so on), nothing more. This is just an observation. And to express the result of the observation by a formula is a formalization.

The interpretation comes later. And concerns with your answer to some possible questions. As an example: why a given property behaves accordingly to the mathematical operation called "sum"?

It seems to me that you are mixing generalizations with peculiarities.

I means, the word "fiinger" is a generalization. It is fine to indicate any arbitrary finger. And in counting any finger is just a finger. More specifically, each finger is not a finger (strictly speaking). It has been traslated into a symbol for unity. And then you are assuming the the arithmetic sum rule holds. If you are interested in a specific finger you can use the words "thumb", "index" and so on. But in such a way you lose the generality and you cannot use them for counting.

The same for apple. If I use the word apple in a general context, I am asserting in one word that the object is a fruit, more specifically is a pomaceous fruit from a rose family tree, etc. etc. If I am interested in a peculiar apple, or if I am interested to address the peculiarities of a specific kind of apple then I will point out the specific properties of that specific apple. But now any my sentence will be valid only locally, I means for the kind of apple I indicated. At the limit, for a specific apple. But if I am only interested in the path followed from a falling apple, to talk just about apples is the correct generalization,

The same when I use the word "mammals" to indicate a clade of endothermic amniotes. So I can formulate phrases as "there exist N different species of mammals", without any need of enumerating each specie.

The same occurs with mathematical formalism. When I state the convention that each letter represents a number, I can write "sentences" as a2-b2=(a+b)(a-b). It is quite obvious that this "sentence" has the same mening of c2-d2=(c-d)(c+d). I do not need to produce all the possible sentences raising from all the possible permutations of letters. And I do not need to produce the sentence where each symbol is substituted by any possible number. This would be an impossible task, But the generalization allow me for understanding the situation, it is not ambiguous and I can produce other "sentences" that are the consequence of the original one. And all the other sentences will be of general validity. 

Entering the realm of philosophy means an abstract level and there exist lot of discussion between supporters and opponents of each philosophy. For a majority of research projects however, the hypothetico-deductive method is an appropriate framework for structuring research process. Scientific research proceeds by formulating a hypothesis that is intended to explain an observation. From this hypothesis some predictions of further phenomena are deduced and tested. Observations that run contrary to those predicted are taken as a conclusive falsification of the hypothesis, observations which are in agreement with those predicted are taken as corroborating the hypothesis

http://www.ruforum.org/sites/default/files/ResearchMethodsResources/research/ResMetRes/3/imgs/hypothetico-deductive%20method.jpg

People that produce hypothesis Z with education background Z might think that finding Z supports hypothesis Z.

Will people with education background X and willing to test hypothesis Z reject hypothesis Z after observing finding Z?

To make it simple: What is called evidence for hypothesis Z in one research field might be rejected as evidence for hypothesis Z in another field? Any examples?

Much time/energy is invested in research aimed to convince “non-believers”. Perhaps “intelligent non-believers” will always be able to find arguments not accepting the scientific interpretations of the results obtained.

Can a hypothesis be produced that is accepted by all humans/scientists, e.g. a hypothesis 100% supported?

Hello All,

I am wondering if we can get 100% of human/scientists to agree on anything! Maybe on something like 2+2=4. 

If we could get 100% it seems to me in theory would have to be a "universal" and possibly one expressed in an if A then B statement, but again 100%? 

Douglas

The process of hypothesis generation is iterative and may pass through several cycles before a valid and precise focused hypothesis is reached. This thinking stage is perhaps the most difficult phase, and certainly the one with which many scientists struggle with most. Use of hypotheses compels a research to clearly and precisely articulate the focus of his/her research. However, some may deliberately choose to avoid the rigours imposed by the precision that is inherent in hypotheses, and opt instead for a less constricting approach centered on research questions or research objectives. Others may have found alternative methods that better suit them, or that are more effective for their particular research area. Different researchers may have their own view point and subjectivity. Practically, no hypothesis is accepted unanimously.

If the process of hypothesis generation is iterative and may pass through several cycles, what is the substantial difference between an hypothesis and an idea? Is the difference reflected in background knowledge available?